54 research outputs found
Arrangements of hyperplanes II: Szenes formula and Eisenstein series
The aim of this article is to generalize in several variables some formulae
for Eisenstein series in one variable. For example the formula for the
values of zeta functions at even integers in functions of Bernoulli numbers. A.
Szenes proved in several variables a similar residue formula for the values of
the zeta function introduced by Witten. We introduce some Eisenstein series by
averaging over a lattice rational functions with poles in an arrangement of
hyperplanes. We give another proof of Szenes residue formula by relating it to
the constant term of these Eisenstein series.Comment: revised version (introduction rewritten, references added, minor
changes made), 28 pages, LaTEX2
The equivariant Todd genus of a complete toric variety, with Danilov condition
We write the equivariant Todd class of a general complete toric variety as an
explicit combination of the orbit closures, the coefficients being analytic
functions on the Lie algebra of the torus which satisfy Danilov's requirement
Discrete series representations and K multiplicities for U(p,q). User's guide
This document is a companion for the Maple program : Discrete series and
K-types for U(p,q) available on:http://www.math.jussieu.fr/~vergne We explain
an algorithm to compute the multiplicities of an irreducible representation of
U(p)x U(q) in a discrete series of U(p,q). It is based on Blattner's formula.
We recall the general mathematical background to compute Kostant partition
functions via multidimensional residues, and we outline our algorithm. We also
point out some properties of the piecewise polynomial functions describing
multiplicities based on Paradan's results.Comment: 51 page
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