111 research outputs found
Inequalities for Moment Cones of Finite-Dimensional Representations
We give a general description of the moment cone associated with an arbitrary
finite-dimensional unitary representation of a compact, connected Lie group in
terms of finitely many linear inequalities. Our method is based on combining
differential-geometric arguments with a variant of Ressayre's notion of a
dominant pair. As applications, we obtain generalizations of Horn's
inequalities to arbitrary representations, new inequalities for the one-body
quantum marginal problem in physics, which concerns the asymptotic support of
the Kronecker coefficients of the symmetric group, and a geometric
interpretation of the Howe-Lee-Tan-Willenbring invariants for the tensor
product algebra.Comment: 42 pages, to appear in Journal of Symplectic Geometr
Local Euler-Maclaurin formula for polytopes
We give a local Euler-Maclaurin formula for rational convex polytopes in a
rational euclidean space . For every affine rational polyhedral cone C in a
rational euclidean space W, we construct a differential operator of infinite
order D(C) on W with constant rational coefficients, which is unchanged when C
is translated by an integral vector. Then for every convex rational polytope P
in a rational euclidean space V and every polynomial function f (x) on V, the
sum of the values of f(x) at the integral points of P is equal to the sum, for
all faces F of P, of the integral over F of the function D(N(F)).f, where we
denote by N(F) the normal cone to P along F.Comment: Revised version (July 2006) has some changes of notation and
references adde
Quillen's relative Chern character is multiplicative
In the 80's, Quillen constructed a de Rham relative cohomology class
associated to a smooth morphism between vector bundles, that we call the
relative Quillen Chern character. In the first part of this paper we prove the
multiplicativ property of the relative Quillen Chern character. Then we obtain
a Riemann-Roch formula between the relative Chern character of the Bott
morphism and the relative Thom form.Comment: 28 pages. This article will appear in the proceedings of the
conference "Algebraic Analysis and Around" in honour of Professor Masaki
Kashiwara's 60's birthda
The multiplicities of the equivariant index of twisted Dirac operators
In this note, we give a geometric expression for the multiplicities of the
equivariant index of a Dirac operator twisted by a line bundle.Comment: 8 page
Index of transversally elliptic operators
In 1996, Berline and Vergne gave a cohomological formula for the index of a
transversally elliptic operator. In this paper we propose a new point of view
where the cohomological formulae make use of equivariant Chern characters with
generalized coefficients and with compact suppport. This kind of Chern
characters was studied by the authors in a previous paper (see
arXiv:0801.2822).Comment: 41 page
Multiple Bernoulli series and volumes of moduli spaces of flat bundles over surfaces
Using Szenes formula for multiple Bernoulli series we explain how to compute
Witten series associated to classical Lie algebras. Particular instances of
these series compute volumes of moduli spaces of flat bundles over surfaces,
and also certain multiple zeta values.Comment: 51 pages, 3 figures; formula in Proposition 3.1 for the Lie group of
type G_2 is corrected; new references adde
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