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Journal of Lie Theory 26 (2016), No. 3, 889--910
Copyright Heldermann Verlag 2016

Algebraic Dirac Induction for Nonholomorphic Discrete Series of SU(2,1)

Ana Prlic
Dept. of Mathematics, University of Zagreb, Bijenicka cesta 30, Zagreb 10000, Croatia

In a joint paper P. Pandzic and D. Renard [Dirac induction for Harish-Chandra modules, J. Lie Theory 20 (2010) 617--641] 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.

Keywords: Lie group, Lie algebra, discrete series, highest weight, minimal K-type, Dirac operator, Dirac cohomology, Dirac induction.

MSC: 22E47; 22E46

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