id
string | text
string | len_category
string | source
string |
|---|---|---|---|
math/0212260
|
We consider a class of measures called autophage which was introduced and
studied by Szekely for measures on the real line. We show that the autophage
measures on finite-dimensional vector spaces over real or p-adic field are
infinitely divisible without idempotent factors and are absolutely continuous
with bounded continuous density. We also show that certain semistable measures
on such vector spaces are absolutely continuous.
|
lt256
|
arxiv_abstracts
|
math/0212261
|
In arXiv math.MG/0207296 we introduced a product construction for locally
compact, complete, geodesic hyperbolic metric spaces. In the present paper we
define the hyperbolic product for general Gromov-hyperbolic spaces. In the case
of roughly geodesic spaces we also analyse the boundary at infinity.
|
lt256
|
arxiv_abstracts
|
math/0212262
|
The aim of this paper is the determination of the largest $n$-dimensional
polytope with $n+3$ vertices of unit diameter. This is a special case of a more
general problem proposed by Graham.
|
lt256
|
arxiv_abstracts
|
math/0212263
|
We study the asymptotic behaviour of solutions to semi-classical nonlinear
Schrodinger equations with a potential, for concentrating and oscillating
initial data, when the nonlinearity is repulsive and the potential is a
polynomial of degree at most two. We describe the separate roles of the
nonlinearity and of the potential, with tools which seem to be specific to the
class of potentials that we consider. We also discuss the case of more general
subquadratic potentials.
|
lt256
|
arxiv_abstracts
|
math/0212264
|
A list of known quantum spheres of dimension one, two and three is presented.
|
lt256
|
arxiv_abstracts
|
math/0212265
|
In the process of developing the theory of free probability and free entropy,
Voiculescu introduced in 1991 a random matrix model for a free semicircular
system. Since then, random matrices have played a key role in von Neumann
algebra theory (cf. [V8], [V9]). The main result of this paper is the following
extension of Voiculescu's random matrix result: Let X_1^(n),...,X_r^(n) be a
system of r stochastically independent n by n Gaussian self-adjoint random
matrices as in Voiculescu's random matrix paper [V4], and let (x_1,...,x_r) be
a semi-circular system in a C*-probability space. Then for every polynomial p
in r noncommuting variables lim_{n->oo}||p(X_1^(n),...,X_r^(n))|| =
||p(x_1,...,x_r)||, for almost all omega in the underlying probability space.
We use the result to show that the Ext-invariant for the reduced C*-algebra of
the free group on 2 generators is not a group but only a semi-group. This
problem has been open since Anderson in 1978 found the first example of a
C*-algebra A for which Ext(A) is not a group.
|
256
|
arxiv_abstracts
|
math/0212266
|
This is an introduction to gerbes for topologists, with emphasis on
non-abelian cohomology.
|
lt256
|
arxiv_abstracts
|
math/0212267
|
Define $I_n^k(\alpha)$ to be the set of involutions of $\{1,2,...,n\}$ with
exactly $k$ fixed points which avoid the pattern $\alpha \in S_i$, for some $i
\geq 2$, and define $I_n^k(\emptyset;\alpha)$ to be the set of involutions of
$\{1,2,...,n\}$ with exactly $k$ fixed points which contain the pattern $\alpha
\in S_i$, for some $i \geq 2$, exactly once. Let $i_n^k(\alpha)$ be the number
of elements in $I_n^k(\alpha)$ and let $i_n^k(\emptyset;\alpha)$ be the number
of elements in $I_n^k(\emptyset;\alpha)$. We investigate $I_n^k(\alpha)$ and
$I_n^k(\emptyset;\alpha)$ for all $\alpha \in S_3$. In particular, we show that
$i_n^k(132)=i_n^k(213)=i_n^k(321)$, $i_n^k(231)=i_n^k(312)$,
$i_n^k(\emptyset;132) =i_n^k(\emptyset;213)$, and
$i_n^k(\emptyset;231)=i_n^k(\emptyset;312)$ for all $0 \leq k \leq n$.
|
lt256
|
arxiv_abstracts
|
math/0212268
|
There exists a smooth foliation with 3 singular points on the two-dimensional
torus such that any lifting of a leaf of this foliation on the universal
covering of the torus is a dense subset of the covering.
|
lt256
|
arxiv_abstracts
|
math/0212269
|
In this note, it is proved that the noise (in the sense of Tsirelson)
generated by a Brownian sticky flow (as defined in math.PR/0211387) is black.
|
lt256
|
arxiv_abstracts
|
math/0212270
|
We organize the nilpotent orbits in the exceptional complex Lie algebras into
series using the triality model and show that within each series the dimension
of the orbit is a linear function of the natural parameter a=1,2,4,8,
respectively for f_4,e_6,e_7,e_8. We also obtain explicit representatives in a
uniform manner. We observe similar regularities for the centralizers of
nilpotent elements in a series and graded components in the associated grading
of the ambient Lie algebra. More strikingly, for a greater than one, the
degrees of the unipotent characters of the corresponding Chevalley groups,
associated to these series through the Springer correspondance are given by
polynomials which have uniform expressions in terms of a.
|
lt256
|
arxiv_abstracts
|
math/0212271
|
The main result is that the fundamental groupoid of the orbit space of a
discontinuous action of a discrete group on a Hausdorff space which admits a
universal cover is the orbit groupoid of the fundamental groupoid of the space.
We also describe work of Higgins and of Taylor which makes this result usable
for calculations. As an example, we compute the fundamental group of the
symmetric square of a space.
The main result, which is related to work of Armstrong, is due to Brown and
Higgins in 1985 and was published in sections 9 and 10 of Chapter 9 of the
first author's book on Topology (Ellis Horwood, 1988). This is a somewhat
edited, and in one point (on normal closures) corrected, version of those
sections. Since the book is out of print, and the result seems not well known,
we now advertise it here.
It is hoped that this account will also allow wider views of these results,
for example in topos theory and descent theory.
Because of its provenance, this should be read as a graduate text rather than
an article. The Exercises should be regarded as further propositions for which
we leave the proofs to the reader. It is expected that this material will be
part of a new edition of the book.
|
256
|
arxiv_abstracts
|
math/0212272
|
We study Harish-Chandra representations of Yangian for gl(2). We prove an
analogue of Kostant theorem showing that resterited Yangians for gl(2) are free
modules over certain maximal commutative subalgebras. We also study the
categories of generic Harish-Chandra modules, describe their simple modules and
indecomposable modules in tame blocks.
|
lt256
|
arxiv_abstracts
|
math/0212273
|
The main motivation for this work was to find an explicit formula for a
"Szego-regularized" determinant of a zeroth order pseudodifferential operator
(PsDO) on a Zoll manifold. The idea of the Szego-regularization was suggested
by V. Guillemin and K. Okikiolu. They have computed the second term in a Szego
type expansion on a Zoll manifold of an arbitrary dimension. In the present
work we compute the third asymptotic term in any dimension. In the case of
dimension 2, our formula gives the above mentioned expression for the
Szego-redularized determinant of a zeroth order PsDO. The proof uses a new
combinatorial identity, which generalizes a formula due to G.A. Hunt and F.J.
Dyson. This identity is related to the distribution of the maximum of a random
walk with i.i.d. steps on the real line. The full version of this paper is also
available, math.FA/0212275.
|
lt256
|
arxiv_abstracts
|
math/0212274
|
We outline the main features of the definitions and applications of crossed
complexes and cubical $\omega$-groupoids with connections. These give forms of
higher homotopy groupoids, and new views of basic algebraic topology and the
cohomology of groups, with the ability to obtain some non commutative results
and compute some homotopy types.
|
lt256
|
arxiv_abstracts
|
math/0212275
|
This is a detailed version of the paper math.FA/0212273. The main motivation
for this work was to find an explicit formula for a "Szego-regularized"
determinant of a zeroth order pseudodifferential operator (PsDO) on a Zoll
manifold. The idea of the Szego-regularization was suggested by V. Guillemin
and K. Okikiolu. They have computed the second term in a Szego type expansion
on a Zoll manifold of an arbitrary dimension. In the present work we compute
the third asymptotic term in any dimension. In the case of dimension 2, our
formula gives the above mentioned expression for the Szego-redularized
determinant of a zeroth order PsDO. The proof uses a new combinatorial
identity, which generalizes a formula due to G.A.Hunt and F.J.Dyson. This
identity is related to the distribution of the maximum of a random walk with
i.i.d. steps on the real line. The proof of this combinatorial identity
together with historical remarks and a discussion of probabilistic and
algebraic connections has been published separately.
|
lt256
|
arxiv_abstracts
|
math/0212276
|
Let X be a noetherian scheme defined over an algebraically closed field of
positive characteristic p, and G be a finite group, of order divisible by p,
acting on X. We introduce a refinement of the equivariant K-theory of X to take
into account the information related to modular representation theory. As an
application, in the 1-dimensional case, we generalize a modular Riemann-Roch
theorem given by S.Nakajima, extending the link between Galois modules and wild
ramification.
|
lt256
|
arxiv_abstracts
|
math/0212277
|
We describe a method of adding tails to C*-correspondences which generalizes
the process used in the study of graph C*-algebras. We show how this technique
can be used to extend results for augmented Cuntz-Pimsner algebras to
C*-algebras associated to general C*-correspondences, and as an application we
prove a gauge-invariant uniqueness theorem for these algebras. We also define a
notion of relative graph C*-algebras and show that properties of these
C*-algebras can provide insight and motivation for results about relative
Cuntz-Pimsner algebras.
|
lt256
|
arxiv_abstracts
|
math/0212278
|
For a positive definite fundamental tensor all known examples of Osserman
algebraic curvature tensors have a typical structure. They can be produced from
a metric tensor and a finite set of skew-symmetric matrices which fulfil
Clifford commutation relations. We show by means of Young symmetrizers and a
theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins that
every algebraic curvature tensor has a structure which is very similar to that
of the above Osserman curvature tensors. We verify our results by means of the
Littlewood-Richardson rule and plethysms. For certain symbolic calculations we
used the Mathematica packages MathTensor, Ricci and PERMS.
|
lt256
|
arxiv_abstracts
|
math/0212279
|
We establish a connection between smooth symplectic resolutions and
symplectic deformations of a (possibly singular) affine Poisson variety.
In particular, let V be a finite-dimensional complex symplectic vector space
and G\subset Sp(V) a finite subgroup. Our main result says that the so-called
Calogero-Moser deformation of the orbifold V/G is, in an appropriate sense, a
versal Poisson deformation. That enables us to determine the algebra structure
on the rational cohomology H^*(X) of any smooth symplectic resolution X \to V/G
(multiplicative McKay correspondence). We prove further that if G is an
irreducible Weyl group in GL(h) and V=h+ h^* then no smooth symplectic
resolution of V/G exists unless G is of types A,B, or C.
|
lt256
|
arxiv_abstracts
|
math/0212280
|
We survey some results concerning finite group actions on products of
spheres.
|
lt256
|
arxiv_abstracts
|
math/0212281
|
We consider the integral of fractional Brownian motion (IFBM) and its
functionals $\xi_T$ on the intervals $(0,T)$ and $(-T,T)$ of the following
types: the maximum $M_T$, the position of the maximum, the occupation time
above zero etc. We show how the asymptotics of $P(\xi_T<1)=p_T, T\to \infty$,
is related to the Hausdorff dimension of Lagrangian regular points for the
inviscid Burgers equation with FBM initial velocity. We produce computational
evidence in favor of a power asymptotics for $p_T$. The data do not reject the
hypothesis that the exponent $\theta$ of the power law is related to the
similarity parameter $H$ of fractional Brownian motion as follows: $\theta
=-(1-H)$ for the interval $(-T,T)$ and $\theta =-H(1-H)$ for $(0,T)$. The point
0 is special in that IFBM and its derivative both vanish there.
|
lt256
|
arxiv_abstracts
|
math/0212282
|
We use $p$-adic families of automorphic forms for an unitary group in three
variables, containing some non-tempered forms constructed by Rogawski, to prove
some cases of the Bloch-Kato conjectures.
|
lt256
|
arxiv_abstracts
|
math/0212283
|
In this paper, we study the following problem $$ \{{ll} \Delta_{H^n}
u-u+u^p=0 & in H^n u>0& in H^n u(x)\to 0 &\rho(x)\to\infty}. $$ where $1<p <
\frac{Q+2}{Q-2}$, Q is the homogeneous dimension of Heisenberg group $H^n$. Our
main result is that this problem has at least one positive solution.
|
lt256
|
arxiv_abstracts
|
math/0212284
|
We consider the class of groups called identity excluding which has the
property that any non-trivial irreducible unitary representation restricted to
a dense subgroup does not weakly contain the trivial representation. For
adapted and strictly aperiodic probability measures on these groups, it is
known that the averages of unitary representations converge strongly. We show
that motion group of a totally disconnected nilpotent group and certain class
of p-adic algebraic groups which includes gruops whose solvable radical is type
R are identity excluding. We also prove the convergence of averages of unitary
representations for split solvable algebraic groups, which are not necessarily
identity excluding.
|
lt256
|
arxiv_abstracts
|
math/0212285
|
A Markov operator $P$ on a $\sigma$-finite measure space $(X, \Sigma, m)$
with invariant measure $m$ is said to have Krengel-Lin decomposition if $L^2
(X) = E_0 \oplus L^2 (X,\Sigma_d)$ where $E_0 = \{f \in L^2 (X) \mid ||P^n (f)
|| \ra 0 \}$ and $\Sigma_d$ is the deterministic $\sigma $-field of $P$. We
consider convolution operators and we show that a measure $\lam$ on a
hypergroup has Krengel-Lin decomposition if and only if the sequence $(\check
\lam ^n *\lam ^n)$ converges to an idempotent or $\lam$ is scattered. We verify
this condition for probabilities on Tortrat groups, on commutative hypergroups
and on central hypergroups. We give a counter-example to show that the
decomposition is not true for measures on discrete hypergroups which is in
contrast to the discrete groups case.
|
lt256
|
arxiv_abstracts
|
math/0212286
|
The theta correspondence has been an important tool in studying cycles in
locally symmetric spaces of orthogonal type. In this paper, we establish for
O(p,2) an adjointness result between Borcherds' singular theta lift and the
Kudla-Millson theta lift. We extend this result to arbitrary signature by
introducing a new Borcherds lift for O(p,q). On the geometric side, this lift
can be interpreted as a differential character in the sense of Cheeger and
Simons.
|
lt256
|
arxiv_abstracts
|
math/0212287
|
In this paper an autonomous analytical system of ordinary differential
equations is considered. For an asymptotically stable steady state x0 of the
system a gradual approximation of the domain of attraction DA is presented in
the case when the matrix of the linearized system in x0 is diagonalizable. This
technique is based on the gradual extension of the "embryo" of an analytic
function of several complex variables. The analytic function is the transformed
of a Lyapunov function whose natural domain of analyticity is the DA and which
satisfies a linear non-homogeneous partial differential equation. The equation
permits to establish an "embryo" of the transformed function and a first
approximation of DA. The "embryo" is used for the determination of a new
"embryo" and a new part of the DA. In this way, computing new "embryos" and new
domains, the DA is gradually approximated. Numerical examples are given for
polynomial systems. For systems considered recently in the literature the
results are compared with those obtained with other methods.
|
256
|
arxiv_abstracts
|
math/0212288
|
We study the validity of geometric optics in $L^\infty$ for nonlinear wave
equations in three space dimensions whose solutions, pulse like, focus at a
point. If the amplitude of the initial data is subcritical, then no nonlinear
effect occurs at leading order. If the amplitude of the initial data is
sufficiently big, strong nonlinear effects occur; we study the cases where the
equation is either dissipative or accretive. When the equation is dissipative,
pulses are absorbed before reaching the focal point. When the equation is
accretive, the family of pulses becomes unbounded.
|
lt256
|
arxiv_abstracts
|
math/0212289
|
In the setting of $\R^d$ with an $n-$dimensional measure $\mu,$ we give
several characterizations of Lipschitz spaces in terms of mean oscillations
involving $\mu.$ We also show that Lipschitz spaces are preserved by those
Calderon-Zygmund operators $T$ associated to the measure $\mu$ for which T(1)
is the Lipschitz class $0.$
|
lt256
|
arxiv_abstracts
|
math/0212290
|
Soit F un corps local non archimedien de caracteristique residuelle p. On
designe par R un corps algebriquement clos de caracteristique p et par Q une
cloture algebrique du corps des nombres p-adiques. On classifie les modules
simples de dimension finie de la R-algebre de Hecke-Iwahori du groupe lineaire
Gl_3(F). Ils sont obtenus par reduction modulo p des modules simples de la
Q-algebre de Hecke-Iwahori qui possedent une structure entiere.
|
lt256
|
arxiv_abstracts
|
math/0212291
|
The article deals with electrodynamics in the presence of anisotropic
materials having scalar wave impedance. Maxwell's equations written for
differential forms over a 3-manifold are analysed. The system is extended to a
Dirac type first order elliptic system on the Grassmannian bundle over the
manifold. The second part of the article deals with the dynamical inverse
boundary value problem of determining the electromagnetic material parameters
from boundary measurements. By using the boundary control method, it is proved
that the dynamical boundary data determines the electromagnetic travel time
metric as well as the scalar wave impedance on the manifold. This invariant
result leads also to a complete characterization of the non-uniqueness of the
corresponding inverse problem in bounded domains of R^3.
AMS-classifications: 35R30, 35L20, 58J45
|
lt256
|
arxiv_abstracts
|
math/0212292
|
Hilbert space representations of the cross product *-algebra of the Hopf
*-algebra U_q(su_2) and its module *-algebras O(S^2_{qc}) of Podles' spheres
are studied. Two classes of representations are described by explicit formulas
for the actions of the generators.
|
lt256
|
arxiv_abstracts
|
math/0212293
|
For $\a,\b>0$ and for a locally integrable function (or, more generally, a
distribution) $\f$ on $(0,\be)$, we study integral ooperators ${\frak
G}^{\a,\b}_\f$ on $L^2(\R_+)$ defined by $\big({\frak G}^{\a,\b}_\f
f\big)(x)=\int_{\R_+}\f\big(x^\a+y^\b\big)f(y)dy$. We describe the bounded and
compact operators ${\frak G}^{\a,\b}_\f$ and operators ${\frak G}^{\a,\b}_\f$
of Schatten--von Neumann class $\bS_p$. We also study continuity properties of
the averaging projection $\Q_{\a,\b}$ onto the operators of the form ${\frak
G}^{\a,\b}_\f$. In particular, we show that if $\a\le\b$ and $\b>1$, then
${\frak G}^{\a,\b}_\f$ is bounded on $\bS_p$ if and only if
$2\b(\b+1)^{-1}<p<2\b(\b-1)^{-1}$.
|
lt256
|
arxiv_abstracts
|
math/0212294
|
We consider subsemimodules and convex subsets of semimodules over semirings
with an idempotent addition. We introduce a nonlinear projection on
subsemimodules: the projection of a point is the maximal approximation from
below of the point in the subsemimodule. We use this projection to separate a
point from a convex set. We also show that the projection minimizes the
analogue of Hilbert's projective metric. We develop more generally a theory of
dual pairs for idempotent semimodules. We obtain as a corollary duality results
between the row and column spaces of matrices with entries in idempotent
semirings. We illustrate the results by showing polyhedra and half-spaces over
the max-plus semiring.
|
lt256
|
arxiv_abstracts
|
math/0212295
|
We present a new approach to Morse and Novikov theories, based on the deRham
Federer theory of currents, using the finite volume flow technique of Harvey
and Lawson. In the Morse case, we construct a noncompact analogue of the Morse
complex, relating a Morse function to the cohomology with compact forward
supports of the manifold. This complex is then used in Novikov theory, to
obtain a geometric realization of the Novikov Complex as a complex of currents
and a new characterization of Novikov Homology as cohomology with compact
forward supports. Two natural ``backward-forward'' dualities are also
established: a Lambda duality over the Novikov Ring and a Topological Vector
Space duality over the reals.
|
lt256
|
arxiv_abstracts
|
math/0212296
|
Stochastic processes on manifolds over non-Archimedean fields and with
transition measures having values in the field $\bf C$ of complex numbers are
defined and investigated. The analogs of Markov, Poisson and Wiener processes
are studied. For Poisson processes the non-Archimedean analog of the L\`evy
theorem is proved. Stochastic antiderivational equations as well as
pseudodifferential equations on manifolds are investigated.
|
lt256
|
arxiv_abstracts
|
math/0212297
|
We utilize the obstruction theory of Galewski-Matumoto-Stern to derive
equivalent formulations of the Triangulation Conjecture. For example, every
closed topological manifold M^n with n > 4 can be simplicially triangulated if
and only if the two distinct combinatorial triangulations of RP^5 are
simplicially concordant.
|
lt256
|
arxiv_abstracts
|
math/0212298
|
Let O be a three-dimensional Nil-orbifold, with branching locus a knot Sigma
transverse to the Seifert fibration. We prove that O is the limit of hyperbolic
cone manifolds with cone angle in (pi-epsilon, pi). We also study the space of
Dehn filling parameters of O-Sigma. Surprisingly it is not diffeomorphic to the
deformation space constructed from the variety of representations of O-Sigma.
As a corollary of this, we find examples of spherical cone manifolds with
singular set a knot that are not locally rigid. Those examples have large cone
angles.
|
lt256
|
arxiv_abstracts
|
math/0212299
|
We consider the set of the power non-negative polynomials of several
variables and its subset that consists of polynomials which can be represented
as a sum of squares. It is shown in the classic work by D.Hilbert that it is a
proper subset. Both sets are convex. In our paper we have made an attempt to
work out a general approach to the investigation of the extremal elements of
these convex sets. We also consider the class of non-negative rational
functions. The article is based on the following methods: 1.We investigate
non-negative trigonometrical polynomials and then with the help of the Calderon
transformation we proceed to the power polynomials. 2.The way of constructing
support hyperplanes to the convex sets is given in the paper.
|
lt256
|
arxiv_abstracts
|
math/0212300
|
We study the formation/dissolution of equilibrium droplets in finite systems
at parameters corresponding to phase coexistence. Specifically, we consider the
2D Ising model in volumes of size $L^2$, inverse temperature $\beta>\betac$ and
overall magnetization conditioned to take the value $\mstar L^2-2\mstar v_L$,
where $\betac^{-1}$ is the critical temperature, $\mstar=\mstar(\beta)$ is the
spontaneous magnetization and $v_L$ is a sequence of positive numbers. We find
that the critical scaling for droplet formation/dissolution is when $v_L^{3/2}
L^{-2}$ tends to a definite limit. Specifically, we identify a dimensionless
parameter $\Delta$, proportional to this limit, a non-trivial critical value
$\Deltac$ and a function $\lambda_\Delta$ such that the following holds: For
$\Delta<\Deltac$, there are no droplets beyond $\log L$ scale, while for
$\Delta>\Deltac$, there is a single, Wulff-shaped droplet containing a fraction
$\lambda_\Delta\ge\lamc=2/3$ of the magnetization deficit and there are no
other droplets beyond the scale of $\log L$. Moreover, $\lambda_\Delta$ and
$\Delta$ are related via a universal equation that apparently is independent of
the details of the system.
|
256
|
arxiv_abstracts
|
math/0212301
|
The calculation of volumes of polyhedra in the three-dimensional Euclidean,
spherical and hyperbolic spaces is very old and difficult problem. In
particular, an elementary formula for volume of non-euclidean simplex is still
unknown. One of the simplest polyhedra is the Lambert cube
Q(\alpha,\beta,\gamma). By definition, Q(\alpha,\beta,\gamma) is a
combinatorial cube, with dihedral angles \alpha,\beta and \gamma assigned to
the three mutually non-coplanar edges and right angles to the remaining. The
hyperbolic volume of Lambert cube was found by Ruth Kellerhals (1989) in terms
of the Lobachevsky function \Lambda(x). In the present paper the spherical
volume of Q(\alpha,\beta,\gamma) is defined in the terms of the function
\delta(\alpha,\theta) which can be considered as a spherical analog of the
Lobachevsky function \Delta(\alpha,\theta)=\Lambda(\alpha + \theta) -
\Lambda(\alpha - \theta)
|
lt256
|
arxiv_abstracts
|
math/0212302
|
The paper investigates higher dimensional analogues of Burago's inequality
bounding the area of a closed surface by its total curvature. We obtain
sufficient conditions for hypersurfaces in 4-space that involve the Ricci
curvature. We get semi-local variants of the inequality holding in any
dimension that involve domains with non-vanishing Gauss-Kronecker curvature.
The paper also contains inequalities of isoperimetric type involving the total
curvature, as well as a "reverse" isoperimetric inequality for spaces with
constant curvature.
|
lt256
|
arxiv_abstracts
|
math/0212303
|
Let G be a reductive connected p-adic group. With help of the Fourier
inversion formula used in [Une formule de Plancherel pour l'algebre de Hecke
d'un groupe reductif p-adique - V. Heiermann, Comm. Math. Helv. 76, 388-415,
2001] we give a spectral decomposition on G. In particular we deduce from it
essentially that a cuspidal representation of a Levi subgroup M is in the
cuspidal support of a square integrable representation of G, if and only if it
is a pole of Harish-Chandra's \mu-function of order equal to the parabolic rank
of M. This result has been conjectured by A. Silberger in 1978. In more
explicit terms, we show that this condition is necessary and that its
sufficiency is equivalent to a combinatorical property of Harish-Chandra's
\mu-function which appears to be a consequence of a result of E. Opdam. We get
also identities between some linear combinations of matrix coeffieicients.
These identities contain informations on the formel degree of square integrable
representations and on their position in the induced representation.
|
256
|
arxiv_abstracts
|
math/0212304
|
Let f be a newform of weight at least 2 and squarefree level with Fourier
coefficients in a number field K. We give explicit bounds, depending on
congruences of f with other newforms, on the set of primes lambda of K for
which the deformation problem associated to the mod lambda Galois
representation of f is obstructed. We include some explicit examples.
|
lt256
|
arxiv_abstracts
|
math/0212305
|
We clarify the exposition of Phases 2 and 3a in "The Floyd-Warshall
Algorithm, the AP and the TSP". We also improve and simplify theorem 3.6 . In
line with clarifying the exposition, we change the matrices in examples 3.4 and
3.5 of "The Floyd-Warshall Algorithm, the AP and the TSP II".
|
lt256
|
arxiv_abstracts
|
math/0212306
|
We define analogues of homogeneous coordinate algebras for noncommutative
two-tori with real multiplication. We prove that the categories of standard
holomorphic vector bundles on such noncommutative tori can be described in
terms of graded modules over appropriate homogeneous coordinate algebras. We
give a criterion for such an algebra to be Koszul and prove that the Koszul
dual algebra also comes from some noncommutative two-torus with real
multiplication. These results are based on the techniques of math.QA/0211262
allowing to interpret all the data in terms of autoequivalences of the derived
categories of coherent sheaves on elliptic curves.
|
lt256
|
arxiv_abstracts
|
math/0212307
|
This paper studies state quantization schemes for feedback stabilization of
control systems with limited information. The focus is on designing the least
destabilizing quantizer subject to a given information constraint. We explore
several ways of measuring the destabilizing effect of a quantizer on the
closed-loop system, including (but not limited to) the worst-case quantization
error. In each case, we show how quantizer design can be naturally reduced to a
version of the so-called multicenter problem from locational optimization.
Algorithms for solving such problems are discussed. In particular, an iterative
solver is developed for a novel weighted multicenter problem which most
accurately represents the least destabilizing quantizer design.
|
lt256
|
arxiv_abstracts
|
math/0212308
|
The connection between Riemann surfaces with boundaries and the theory of
vertex operator algebras is discussed in the framework of conformal field
theories defined by Kontsevich and Segal and in the framework of their
generalizations in open string theory and boundary conformal field theory. We
present some results, problems, conjectures, their conceptual implications and
meanings in a program to construct these theories from representations of
vertex operator algebras.
|
lt256
|
arxiv_abstracts
|
math/0212309
|
We give an elementary introduction to some recent polyhedral techniques for
understanding and solving systems of multivariate polynomial equations. We
provide numerous concrete examples and illustrations, and assume no background
in algebraic geometry or convex geometry. Highlights include the following:
(1) A completely self-contained proof of an extension of Bernstein's Theorem.
Our extension relates volumes of polytopes with the number of connected
components of the complex zero set of a polynomial system, and allows any
number of polynomials and/or variables.
(2) A near optimal complexity bound for computing mixed area -- a quantity
intimately related to counting complex roots in the plane.
|
lt256
|
arxiv_abstracts
|
math/0212310
|
We present a general framework for TQFT and related constructions using the
language of monoidal categories. We construct a topological category C and an
algebraic category D, both monoidal, and a TQFT functor is then defined as a
certain type of monoidal functor from C to D. In contrast with the cobordism
approach, this formulation of TQFT is closer in spirit to the classical
functors of algebraic topology, like homology. The fundamental operation of
gluing is incorporated at the level of the morphisms in the topological
category through the notion of a gluing morphism, which we define. It allows
not only the gluing together of two separate objects, but also the self-gluing
of a single object to be treated in the same fashion. As an example of our
framework we describe TQFT's for oriented 2D-manifolds, and classify a family
of them in terms of a pair of tensors satisfying some relations.
|
lt256
|
arxiv_abstracts
|
math/0212311
|
We analyze geometry of the second order differential operators, having in
mind applications to Batalin--Vilkovisky formalism in quantum field theory. As
we show, an exhaustive picture can be obtained by considering pencils of
differential operators acting on densities of all weights simultaneously. The
algebra of densities, which we introduce here, has a natural invariant scalar
product. Using it, we prove that there is a one-to-one correspondence between
second-order operators in this algebra and the corresponding brackets. A
bracket on densities incorporates a bracket on functions, an ``upper
connection'' in the bundle of volume forms, and a term similar to the
``Brans--Dicke field'' of the Kaluza--Klein formalism. These results are valid
for even operators on a usual manifold as well as for odd operators on a
supermanifold. For an odd operator $\Delta$ we show that conditions on the
order of the operator $\Delta^2$ give an hierarchy of properties such as
flatness of the upper connection and the Batalin--Vilkovisky master equation.
In particular, we obtain a complete description of generating operators for an
arbitrary odd Poisson bracket.
|
256
|
arxiv_abstracts
|
math/0212312
|
Marion Scheepers, in his studies of the combinatorics of open covers,
introduced the property Split(U,V) asserting that a cover of type U can be
split into two covers of type V. In the first part of this paper we give an
almost complete classification of all properties of this form where U and V are
significant families of covers which appear in the literature (namely, large
covers, omega-covers, tau-covers, and gamma-covers), using combinatorial
characterizations of these properties in terms related to ultrafilters on N.
In the second part of the paper we consider the questions whether, given U
and V, the property Split(U,V) is preserved under taking finite unions,
arbitrary subsets, powers or products. Several interesting problems remain
open.
|
lt256
|
arxiv_abstracts
|
math/0212313
|
We construct explicitly non-polynomial eigenfunctions of the difference
operators by Macdonald in case $t=q^k$, $k\in{\mathbb Z}$. This leads to a new,
more elementary proof of several Macdonald conjectures, first proved by
Cherednik. We also establish the algebraic integrability of Macdonald operators
at $t=q^k$ ($k\in {\mathbb Z}$), generalizing the result of Etingof and
Styrkas. Our approach works uniformly for all root systems including $BC_n$
case and related Koornwinder polynomials. Moreover, we apply it for a certain
deformation of $A_n$ root system where the previously known methods do not
work.
|
lt256
|
arxiv_abstracts
|
math/0212314
|
We prove the Hodge-D-conjecture for general K3 and Abelian surfaces. Some
consequences of this result, e.g., on the levels of higher Chow groups of
products of elliptic curves, are discussed.
|
lt256
|
arxiv_abstracts
|
math/0212315
|
Let Z be a general surface in P^3 of degree at least 5. Using a Lefschetz
pencil argument, we give an elementary new proof of the vanishing of a
regulator on K_1(Z).
|
lt256
|
arxiv_abstracts
|
math/0212316
|
Witten's gauged linear sigma model [Wi1] is one of the universal frameworks
or structures that lie behind stringy dualities. Its A-twisted moduli space at
genus 0 case has been used in the Mirror Principle [L-L-Y] that relates
Gromov-Witten invariants and mirror symmetry computations. In this paper the
A-twisted moduli stack for higher genus curves is defined and systematically
studied. It is proved that such a moduli stack is an Artin stack. For genus 0,
it has the A-twisted moduli space of [M-P] as the coarse moduli space. The
detailed proof of the regularity of the collapsing morphism by Jun Li in
[L-L-Y: I and II] can be viewed as a natural morphism from the moduli stack of
genus 0 stable maps to the A-twisted moduli stack at genus 0.
Due to the technical demand of stacks to physicists and the conceptual demand
of supersymmetry to mathematicians, a brief introduction of each topic that is
most relevant to the main contents of this paper is given in the beginning and
the appendix respectively. Themes for further study are listed in the end.
|
256
|
arxiv_abstracts
|
math/0212317
|
This is a condensed write-up of a talk delivered at the Ramanujan
International Symposium on Kac-Moody Lie algebras and Applications in Chennai
in January 2002. The talk introduces special coideal subalgebras of quantum
affine algebras which appear in physics when solitons are restricted to live on
a half-line by an integrable boundary condition. We review how the quantum
affine symmetry determines the soliton S-matrix in affine Toda field theory and
then go on to use the unbroken coideal subalgebra on the half-line to determine
the soliton reflection matrix. This gives a representation theoretic method for
the solution of the reflection equation (boundary Yang-Baxter equation) by
reducing it to a linear equation.
|
lt256
|
arxiv_abstracts
|
math/0212318
|
In our previous paper, we constructed an explicit GL(n)-equivariant
quantization of the Kirillov--Kostant-Souriau bracket on a semisimple coadjoint
orbit. In the present paper, we realize that quantization as a subalgebra of
endomorphisms of a generalized Verma module. As a corollary, we obtain an
explicit description of the annihilators of generalized Verma modules over
U(gl(n)). As an application, we construct real forms of the quantum orbits and
classify finite dimensional representations. We compute the non-commutative
Connes index for basic homogenous vector bundles over the quantum orbits.
|
lt256
|
arxiv_abstracts
|
math/0212319
|
We show that in the neighborhood of each ``finite type'' singular orbit of a
real analytic integrable dynamical system (hamiltonian or not) there is a real
analytic torus action which preserves the system and which is transitive on
this orbit. We also show that the local automorphism group of the system near
such an orbit is
|
lt256
|
arxiv_abstracts
|
math/0212320
|
We briefly review and illustrate our procedure to 'decouple' by
transformation of generators: either a Hopf algebra $H$ from a $H$-module
algebra $A_1$ in their cross-product $A_1 >\triangleleft H$; or two (or more)
$H$-module algebras $A_1,A_2$. These transformations are based on the existence
of an algebra map $A_1 >\triangleleft H\to A_1$.
|
lt256
|
arxiv_abstracts
|
math/0212321
|
The main result of this paper amounts to a complete evaluation of the
integral cohomological structure of the stable mapping class group. In
particular it verifies the conjecture of D.Mumford about the rational
cohomology of the stable mapping class group.
|
lt256
|
arxiv_abstracts
|
math/0212322
|
An isoperimetric upper bound on the resistance is given. As a corollary we
resolve two problems, regarding mean commute time on finite graphs and
resistance on percolation clusters. Further conjectures are presented.
|
lt256
|
arxiv_abstracts
|
math/0212323
|
The main purpose of this paper is to investigate the behaviour of fractional
integral operators associated to a measure on a metric space satisfying just a
mild growth condition, namely that the measure of each ball is controlled by a
fixed power of its radius. This allows, in particular, non--doubling measures.
It turns out that this condition is enough to build up a theory that contains
the classical results based upon the Lebesgue measure on euclidean space and
their known extensions for doubling measures. We start by analyzing the images
of the Lebesgue spaces associated to the measure. The Lipschitz spaces, defined
in terms of the metric, play a basic role too. For a euclidean space equipped
with one of these measures, we also consider the so-called `` regular\rq\rq
$\bmo$ space introduced by X. Tolsa. We show that it contains the image of a
Lebesgue space in the appropriate limit case and also that the image of the
space `` regular\rq\rq $\bmo$ is contained in the adequate Lipschitz space.
|
lt256
|
arxiv_abstracts
|
math/0212324
|
The "noncommutative geometry" of complex algebraic curves is studied. As
first step, we clarify a morphism between elliptic curves, or complex tori, and
C*-algebras T_t={u,v | vu=exp(2\pi it)uv}, or noncommutative tori. The main
result says that under the morphism isomorphic elliptic curves map to the
Morita equivalent noncommutative tori. Our approach is based on the rigidity of
the length spectra of Riemann surfaces.
|
lt256
|
arxiv_abstracts
|
math/0212325
|
We propose a variant to the Etingof-Kazhdan construction of quantization
functors. We construct the twistor J_\Phi associated to an associator \Phi
using cohomological techniques. We then introduce a criterion ensuring that the
``left Hopf algebra'' of a quasitriangular QUE algebra is flat. We prove that
this criterion is satisfied at the universal level. This provides a
construction of quantization functors, equivalent to the Etingof-Kazhdan
construction.
|
lt256
|
arxiv_abstracts
|
math/0212326
|
The main goal of this paper is to investigate the structure of Hopf algebras
with the property that either its Jacobson radical is a Hopf ideal or its
coradical is a subalgebra. In order to do that we define the Hochschild
cohomology of an algebra in an abelian monoidal category. Then we characterize
those algebras which have dimension less than or equal to 1 with respect to
Hochschild cohomology. Now let us consider a Hopf algebra A such that its
Jacobson radical J is a nilpotent Hopf ideal and H:=A/J is a semisimple
algebra. By using our homological results, we prove that the canonical
projection of A on H has a section which is an H-colinear algebra map.
Furthermore, if H is cosemisimple too, then we can choose this section to be an
(H,H)-bicolinear algebra morphism. This fact allows us to describe A as a
`generalized bosonization' of a certain algebra R in the category of
Yetter-Drinfeld modules over H. As an application we give a categorical proof
of Radford's result about Hopf algebras with projections. We also consider the
dual situation. In this case, many results that we obtain hold true for a large
enough class of H-module coalgebras, where H is a cosemisimple Hopf algebra.
|
256
|
arxiv_abstracts
|
math/0212327
|
It is shown that the cycle space of an arbitrary orbit of a non-Hermitian
real form G in a flag manifold $Z=G^\mathbb C/Q$ of its complexification is
naturally equivalent to a certain universal domain which depends only on G.
This makes use of complex geometric methods which were recently developed for
the purpose of handling the case of open orbits together with a better
understanding of the connection to Schubert varieties and the related complex
slices along lower-dimensional Gorbits.
|
lt256
|
arxiv_abstracts
|
math/0212328
|
We present a bijection between 321- and 132-avoiding permutations that
preserves the number of fixed points and the number of excedances. This gives a
simple combinatorial proof of recent results of Robertson, Saracino and
Zeilberger, and the first author. We also show that our bijection preserves
additional statistics, which extends the previous results.
|
lt256
|
arxiv_abstracts
|
math/0212329
|
THEOREM. For every prime $p$ and each $n=2, 3, ... \infty$, there is an
action of $G=\prod_{i=1}^{\infty}(Z/ pZ)$ on a two-dimensional compact metric
space $X$ with $n$-dimensional orbit space.
This theorem was proved in [DW: A.N. Dranishnikov and J.E. West, Compact
group actions that raise dimension to infinity, Topology and its Applications
80 (1997), 101-114] with an error in one of the lemmas (Lemma 15). This paper
presents a corrected version of Lemma 15 and it is identical with [DW] in the
rest.
|
lt256
|
arxiv_abstracts
|
math/0212330
|
In math.AG/0207028 we began the study of higher sheaf theory (i.e. stacks
theory) on higher categories endowed with a suitable notion of topology:
precisely, we defined the notions of S-site and of model site, and the
associated categories of stacks on them. This led us to study a notion of
\textit{model topos} (orginally due to C. Rezk), a model category version of
the notion of Grothendieck topos. In this paper we treat the analogous theory
starting from (1-)Segal categories in place of S-categories and model
categories. We introduce notions of Segal topologies, Segal sites and stacks
over them. We define an abstract notion of Segal topos and relate it with Segal
categories of stacks over Segal sites. We compare the notions of Segal topoi
and of model topoi, showing that the two theories are equivalent in some sense.
However, the existence of a nice Segal category of morphisms between Segal
categories allows us to improve the treatment of topoi in this context. In
particular we construct the 2-Segal category of Segal topoi and geometric
morphisms, and we provide a Giraud-like statement characterizing Segal topoi
among Segal categories. As an example of applications, we show how to
reconstruct a topological space up to homotopy from the Segal topos of locally
constant stacks on it, thus extending the main theorem of Toen, "Vers une
interpretation Galoisienne de la theorie de l'homotopie" (to appear in Cahiers
de top. et geom. diff. cat.) to the case of un-based spaces. We also give some
hints of how to define homotopy types of Segal sites: this approach gives a new
point of view and some improvements on the \'etale homotopy theory of schemes,
and more generally on the theory of homotopy types of Grothendieck sites as
defined by Artin and Mazur.
|
256
|
arxiv_abstracts
|
math/0212331
|
$T$-semi-selfdecomposability and subclasses $L_m(b, Q)$ and $\tilde L_m(b,
Q)$ of measures on complete separable metric vector spaces are introduced and
basic properties are proved. In particular, we show that $\mu$ is
$T$-semi-selfdecomposable if and only if $\mu = T(\mu) \nu$ where $\nu$ is
infinitely divisible and $\mu$ is operator selfdecomposable if and only if $\mu
\in L_0(b, Q)$ for all $0< b < 1$.
|
lt256
|
arxiv_abstracts
|
math/0212332
|
In this paper we study left 3-Engel elements in groups. In particular, we
prove that for any prime $p$ and any left 3-Engel element $x$ of finite
$p$-power order in a group $G$, $x^p$ is in the Baer radical of $G$. Also it is
proved that $<x,y>$ is nilpotent of class 4 for every two left 3-Engel elements
in a group $G$.
|
lt256
|
arxiv_abstracts
|
math/0212333
|
In this Note we study the groups $G$ satisfying condition $(\mathcal{N},n)$,
that is, every subset of $G$ with $n+1$ elements contains a pair $\{x,y\}$ such
that the subgroup $<x,y>$ is nilpotent.
|
lt256
|
arxiv_abstracts
|
math/0212334
|
These notes form an extended version of a minicourse delivered in Universite
de Montreal (June 2002) within the framework of a NATO workshop ``Normal Forms,
Bifurcations and Finiteness Problems in Differential Equations''.
The focus is on Poincare--Dulac theory of ``Fuchsian'' (logarithmic)
singularities of integrable systems, with applications to problems on zeros of
Abelian integrals in view.
|
lt256
|
arxiv_abstracts
|
math/0212335
|
A MAD (maximal almost disjoint) family is an infinite subset A of the
infinite subsets of {0,1,2,..} such that any two elements of A intersect in a
finite set and every infinite subset of {0.1.2...} meets some element of $\aa$
in an infinite set. A Q-set is an uncountable set of reals such that every
subset is a relative G-delta set. It is shown that it is relatively consistent
with ZFC that there exists a MAD family which is also a Q-set in the topology
in inherits a subset of the Power set of {0,1,2,..}, ie the Cantor set.
|
lt256
|
arxiv_abstracts
|
math/0212336
|
A subset X of the Cantor space, 2^\omega, is a lambda-prime-set iff for every
countable subset Y of the Cantor space Y is relatively G-delta in X union Y. In
this paper we prove two forcing results about lambda-prime-sets. First we show
that it is consistent that every lambda-prime-set is a gamma-set. Secondly we
show that is independent whether or not every dagger-lambda-set is a
lambda-prime-set.
|
lt256
|
arxiv_abstracts
|
math/0212337
|
In this paper we provide a criterion for the quasi-autonomous Hamiltonian
path (``Hofer's geodesic'') on arbitrary closed symplectic manifolds
$(M,\omega)$ to be length minimizing in its homotopy class in terms of the
spectral invariants $\rho(G;1)$ that the author has recently constructed
(math.SG/0206092). As an application, we prove that any autonomous Hamiltonian
path on arbitrary closed symplectic manifolds is length minimizing in {\it its
homotopy class} with fixed ends, when it has no contractible periodic orbits
{\it of period one}, has a maximum and a minimum point which are generically
under-twisted and all of its critical points are nondegenerate in the Floer
theoretic sense. This is a sequel to the papers math.SG/0104243 and
math.SG/0206092.
|
lt256
|
arxiv_abstracts
|
math/0212338
|
We give an alternative proof of the existence of the scaling limit of loop
erased random walk which does not use Lowner's differential equation.
|
lt256
|
arxiv_abstracts
|
math/0212339
|
Let $(A,\frak m)$ be an excellent normal local ring with algebraically closed
residue class field. Given integrally closed $\frak m$-primary ideals $I\supset
J$, we show that there is a composition series between $I$ and $J$, by
integrally closed ideals only. Also we show that any given integrally closed
$\fm$-primary ideal $I$, the family of integrally closed ideals $J\subset I,
l_A(I/J)=1$ forms an algebraic variety with dimension $\dim A -1$.
|
lt256
|
arxiv_abstracts
|
math/0212340
|
Demailly, Ein and Lazarsfeld \cite{DEL} proved the subadditivity theorem for
multiplier ideals, which states the multiplier ideal of the product of ideals
is contained in the product of the individual multiplier ideals, on
non-singular varieties. We prove that, in two-dimensional case, the
subadditivity theorem holds on log-terminal singularities. However, in higher
dimensional case, we have several counter-examples. We consider the
subadditivity theorem for monomial ideals on toric rings, and construct a
counter-example on a three-dimensional toric ring.
|
lt256
|
arxiv_abstracts
|
math/0212341
|
A basic point about hyperbolic groups is that they have "spaces at infinity"
which are spaces of homogeneous type in the sense of Coifman and Weiss, and
with a lot of self-similarity coming from the group. This short survey deals
with some of the notions involved.
|
lt256
|
arxiv_abstracts
|
math/0212342
|
We give a fast, exact algorithm for solving Dirichlet problems with
polynomial boundary functions on quadratic surfaces in R^n such as ellipsoids,
elliptic cylinders, and paraboloids. To produce this algorithm, first we show
that every polynomial in R^n can be uniquely written as the sum of a harmonic
function and a polynomial multiple of a quadratic function, thus extending a
theorem of Ernst Fischer. We then use this decomposition to reduce the
Dirichlet problem to a manageable system of linear equations. The algorithm
requires differentiation of the boundary function, but no integration. We also
show that the polynomial solution produced by our algorithm is the unique
polynomial solution, even on unbounded domains such as elliptic cylinders and
paraboloids.
|
lt256
|
arxiv_abstracts
|
math/0212343
|
In this article we generalize packing density problems from permutations to
patterns with repeated letters and generalized patterns. We are able to find
the packing density for some classes of patterns and several other short
patterns.
|
lt256
|
arxiv_abstracts
|
math/0212344
|
In this paper we study the average $\NL_{2\alpha}$-norm over $T$-polynomials,
where $\alpha$ is a positive integer. More precisely, we present an explicit
formula for the average $\NL_{2\alpha}$-norm over all the polynomials of degree
exactly $n$ with coefficients in $T$, where $T$ is a finite set of complex
numbers, $\alpha$ is a positive integer, and $n\geq0$. In particular, we give a
complete answer for the cases of Littlewood polynomials and polynomials of a
given height. As a consequence, we derive all the previously known results for
this kind of problems, as well as many new results.
|
lt256
|
arxiv_abstracts
|
math/0212345
|
We prove that some ergodic linear automorphisms of $\T^N$ are stably ergodic,
i.e. any small perturbation remains ergodic. The class of linear automorphisms
we deal with includes all non-Anosov ergodic automorphisms when N=4 and so, as
a corollary, we get that every ergodic linear automorphism of $\T^N$ is stably
ergodic when $N\leq 5$.
|
lt256
|
arxiv_abstracts
|
math/0212346
|
A class of high-order lowpass filters, the discrete singular convolution
(DSC) filters, is utilized to facilitate the Fourier pseudospectral method for
the solution of hyperbolic conservation law systems. The DSC filters are
implemented directly in the Fourier domain (i.e., windowed Fourier
pseudospectral method), while a physical domain algorithm is also given to
enable the treatment of some special boundary conditions. By adjusting the
effective wavenumber region of the DSC filter, the Gibbs oscillations can be
removed effectively while the high resolution feature of the spectral method
can be retained. The utility and effectiveness of the present approach is
validated by extensive numerical experiments.
|
lt256
|
arxiv_abstracts
|
math/0212347
|
We obtain the fermionic formulas for the characters of (k, r)-admissible
configurations in the case of r=2 and r=3. This combinatorial object appears as
a label of a basis of certain subspace $W(\Lambda)$ of level-$k$ integrable
highest weight module of $\hat{sl}_{r}$. The dual space of $W(\Lambda)$ is
embedded into the space of symmetric polynomials. We introduce a filtration on
this space and determine the components of the associated graded space
explicitly by using vertex operators. This implies a fermionic formula for the
character of $W(\Lambda)$.
|
lt256
|
arxiv_abstracts
|
math/0212348
|
For all $k$, we construct a bijection between the set of sequences of
non-negative integers ${\bf a}=(a_i)_{i\in{\bf Z}_{\geq0}}$ satisfying
$a_i+a_{i+1}+a_{i+2}\leq k$ and the set of rigged partitions $(\lambda,\rho)$.
Here $\lambda=(\lambda_1,...,\lambda_n)$ is a partition satisfying
$k\geq\lambda_1\geq...\geq\lambda_n\geq1$ and $\rho=(\rho_1,...,\rho_n)\in{\bf
Z}_{\geq0}^n$ is such that $\rho_j\geq\rho_{j+1}$ if $\lambda_j=\lambda_{j+1}$.
One can think of $\lambda$ as the particle content of the configuration ${\bf
a}$ and $\rho_j$ as the energy level of the $j$-th particle, which has the
weight $\lambda_j$. The total energy $\sum_iia_i$ is written as the sum of the
two-body interaction term $\sum_{j<j'}A_{\lambda_j,\lambda_{j'}}$ and the free
part $\sum_j\rho_j$. The bijection implies a fermionic formula for the
one-dimensional configuration sums $\sum_{\bf a}q^{\sum_iia_i}$. We also derive
the polynomial identities which describe the configuration sums corresponding
to the configurations with prescribed values for $a_0$ and $a_1$, and such that
$a_i=0$ for all $i>N$.
|
256
|
arxiv_abstracts
|
math/0212349
|
Let $X$ be the exterior of connected sum of knots and $X_i$ the exteriors of
the individual knots. In \cite{morimoto1} Morimoto conjectured (originally for
$n=2$) that $g(X) < \sigma_{i=1}^n g(X_i)$ if and only if there exists a
so-called \em primitive meridian \em in the exterior of the connected sum of a
proper subset of the knots. For m-small knots we prove this conjecture and
bound the possible degeneration of the Heegaard genus (this bound was
previously achieved by Morimoto under a weak assumption \cite{morimoto2}):
$$\sigma_{i=1}^n g(X_i) - (n-1) \leq g(X) \leq \sigma_{i=1}^n g(X_i).$$
|
lt256
|
arxiv_abstracts
|
math/0212350
|
In this paper we will discuss a procedure to improve the usual estimator of a
linear functional of the unknown regression function in inverse nonparametric
regression models. In Klaassen, Lee, and Ruymgaart (2001) it has been proved
that this traditional estimator is not asymptotically efficient (in the sense
of the H\'{a}jek - Le Cam convolution theorem) except, possibly, when the error
distribution is normal. Since this estimator, however, is still root-n
consistent a procedure in Bickel, Klaassen, Ritov, and Wellner (1993) applies
to construct a modification which is asymptotically efficient. A self-contained
proof of the asymptotic efficiency is included.
|
lt256
|
arxiv_abstracts
|
math/0212351
|
Call {\em i-hedrite} any 4-valent n-vertex plane graph, whose faces are 2-,
3- and 4-gons only and $p_2+p_3=i$. The edges of an i-hedrite, as of any
Eulerian plane graph, are partitioned by its {\em central circuits}, i.e.
those, which are obtained by starting with an edge and continuing at each
vertex by the edge opposite the entering one. So, any i-hedrite is a projection
of an alternating link, whose components correspond to its central circuits.
Call an i-hedrite {\em irreducible}, if it has no {\em rail-road}, i.e. a
circuit of 4-gonal faces, in which every 4-gon is adjacent to two of its
neighbors on opposite edges.
We present the list of all i-hedrites with at most 15 vertices. Examples of
other results:
(i) All i-hedrites, which are not 3-connected, are identified. (ii) Any
irreducible i-hedrite has at most i-2 central circuits. (iii) All i-hedrites
without self-intersecting central circuits are listed. (iv) All symmetry group
of i-hedrites are listed.
|
lt256
|
arxiv_abstracts
|
math/0212352
|
A zigzag in a plane graph is a circuit of edges, such that any two, but no
three, consecutive edges belong to the same face. A railroad in a plane graph
is a circuit of hexagonal faces, such that any hexagon is adjacent to its
neighbors on opposite edges. A graph without a railroad is called tight. We
consider the zigzag and railroad structures of general 3-valent plane graph
and, especially, of simple two-faced polyhedra, i.e., 3-valent 3-polytopes with
only $a$-gonal and $b$-gonal faces, where $3 \le a < b \le 6$; the main cases
are $(a,b)=(3,6)$, $(4,6)$ and $(5,6)$ (the fullerenes).
We completely describe the zigzag structure for the case $(a,b)$=$(3,6)$. For
the case $(a,b)$=$(4,6)$ we describe symmetry groups, classify all tight graphs
with simple zigzags and give the upper bound 9 for the number of zigzags in
general tight graphs. For the remaining case $(a,b)$=$(5,6)$ we give a
construction realizing a prescribed zigzag structure.
|
lt256
|
arxiv_abstracts
|
math/0212353
|
Given a lattice $L$, a full dimensional polytope $P$ is called a {\em
Delaunay polytope} if the set of its vertices is $S\cap L$ with $S$ being an
{\em empty sphere} of the lattice. Extending our previous work \cite{DD-hyp} on
the {\em hypermetric cone} $HYP_7$, we classify the six-dimensional Delaunay
polytopes according to their {\em combinatorial type}. The list of 6241
combinatorial types is obtained by a study of the set of faces of the
polyhedral cone $HYP_7$.
|
lt256
|
arxiv_abstracts
|
math/0212354
|
We consider odd Laplace operators arising in odd symplectic geometry.
Approach based on semidensities (densities of weight 1/2) is developed. The
role of semidensities in the Batalin--Vilkovisky formalism is explained. In
particular, we study the relations between semidensities on an odd symplectic
supermanifold and differential forms on a purely even Lagrangian submanifold.
We establish a criterion of ``normality'' of a volume form on an odd symplectic
supermanifold in terms of the canonical odd Laplacian acting on semidensities.
|
lt256
|
arxiv_abstracts
|
math/0212355
|
Let $(M, \dr M)$ be a 3-manifold with incompressible boundary that admits a
convex co-compact hyperbolic metric. We consider the hyperbolic metrics on $M$
such that $\dr M$ looks locally like a hyperideal polyhedron, and we
characterize the possible dihedral angles.
We find as special cases the results of Bao and Bonahon on hyperideal
polyhedra, and those of Rousset on fuchsian hyperideal polyhedra. Our results
can also be stated in terms of circle configurations on $\dr M$, they provide
an extension of the Koebe theorem on circle packings.
The proof uses some elementary properties of the hyperbolic volume, in
particular the Schl\"afli formula and the fact that the volume of (truncated)
hyperideal simplices is a concave function of the dihedral angles.
|
lt256
|
arxiv_abstracts
|
math/0212356
|
For any pair of integers $n\geq 1$ and $q\geq 2$, we construct an infinite
family of mutually non-isotopic symplectic tori representing the homology class
$q[F]$ of an elliptic surface E(n), where $[F]$ is the homology class of the
fiber. We also show how such families can be non-isotopically and
symplectically embedded into a more general class of symplectic 4-manifolds.
|
lt256
|
arxiv_abstracts
|
math/0212357
|
We extend the setup in our previous paper to deal with the case in which more
than one steady state may exist in feedback configurations. This provides a
foundation for the analysis of multi-stability and hysteresis behaviour in high
dimensional feedback systems.
|
lt256
|
arxiv_abstracts
|
math/0212358
|
This paper explains the conjectured algebraic duality between genus zero
Gromov-Witten theory and genus zero "Closed String topology". This duality in
another perspective is discussed on page 87 of the book "Frobenius manifold,
quantum cohomology, and moduli spaces" (by Yuri Manin). This paper also
discusses Fulton MacPherson strata.
|
lt256
|
arxiv_abstracts
|
math/0212359
|
We analyze the structure of co-invariant subspaces for representations of the
Cuntz algebras O_N for N = 2,3,..., N < infinity, with special attention to the
representations which are associated to orthonormal and tight-frame wavelets in
L^2(R) corresponding to scale number N.
|
lt256
|
arxiv_abstracts
|
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