Characters of averaged discrete series on semisimple real Lie groups

Abstract

Let G be a real simple Lie group of classical type having a compact Car tan subgroup. Then G has discrete series representations. The purpose of this paper is to establish explicit formulas for certain sums of discrete series characters. These "averaged'* discrete series characters have simple formulas which can be used for certain problems in harmonic analysis on G, for example, for the computation of the Plancherel measure on G.