Dirac series for complex classical Lie groups: A multiplicity-one theorem

Abstract

This paper computes the Dirac cohomology $H_D(\pi )$ of irreducible unitary Harish-Chandra modules $\pi$ of complex classical groups viewed as real reductive groups. More precisely, unitary representations with nonzero Dirac cohomology are shown to be unitarily induced from unipotent representations. When nonzero, there is a unique, multiplicity free $K-$type in $\pi$ contributing to $H_D(\pi )$. This confirms conjectures formulated by the first named author and Pandzic in 2011.

42 pages, to appear in Adv. Math