Characters of averaged discrete series on semisimple real Lie groups

Rebecca A. Herb

Vol. 80 (1979), No. 1, 169–177

DOI: 10.2140/pjm.1979.80.169

Abstract

Let G be a real simple Lie group of classical type having a compact Cartan 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 Ĝ.

Mathematical Subject Classification 2000

Primary: 22E46

Milestones

Received: 6 March 1978

Published: 1 January 1979