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

Understand

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.