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

TL;DR

This paper extends the algebraic Dirac induction method to construct nonholomorphic discrete series representations of SU(2,1), broadening the understanding of representation theory for this group.

Contribution

It introduces a novel approach to construct nonholomorphic discrete series of SU(2,1) using algebraic Dirac induction, complementing previous results for holomorphic and antiholomorphic cases.

Findings

Nonholomorphic discrete series can be constructed via algebraic Dirac induction.

The method generalizes previous constructions for holomorphic and antiholomorphic series.

Provides new tools for representation theory 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.