Construction of discrete series representations of via algebraic Dirac induction

Abstract

The notion of algebraic Dirac induction was introduced by P. Pandžić and D. Renard. This is a construction which gives representations with prescribed Dirac cohomology. They proved that all holomorphic discrete series representations can be constructed via Dirac induction. All discrete series representations of the group are nonholomorphic. In this paper we prove that they can also be constructed using algebraic Dirac induction.Communicated by Silvana Bazzoni