Discrete series representations and K multiplicities for U(p,q). User's guide

Details Discrete series representations and K multiplicities for U(p,q). User's guide Discrete series representations and K multiplicities for U(p,q). User's guide

2010-08-31

arxiv.org/abs/1008.5360v1

Mathematics

Combinatorics

51 pages

Scientific paper

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.

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