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Journal of Lie Theory 25 (2015), No. 1, 185--213
Copyright Heldermann Verlag 2015

Dirac Cohomology of Unipotent Representations of Sp(2n,R) and U(p,q)

Dan Barbasch
Department of Mathematics, Cornell University, Ithaca, NY 14850, U.S.A.

Pavle Pandzic
Department of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, Croatia

We compute the Dirac cohomology of the special unipotent representations of the real groups Sp(2n,R) and U(p,q). Unlike the simpler cases treated in the literature so far, the answer here is quite involved. In particular, the Dirac cohomology can contain K-types with high multiplicity.

Keywords: Lie group, Lie algebra, representation, special unipotent representation, Dirac operator, Dirac cohomology.

MSC: 22E47; 22E46

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