Algebraic Dirac induction for nonholomorphic discrete series of SU(2, 1)

Abstract

In a joint paper P. Pand\v{z}i\'c and D. Renard proved that holomorphic and antiholomorphic discrete series representations can be constructed via algebraic Dirac induction. The group $SU(2,1)$, except for those two types, also has a third type of discrete series representations that are neither holomorphic nor antiholomorphic. In this paper we show that nonholomorphic discrete series representations of the group $SU(2,1)$ can also be constructed using algebraic Dirac induction.