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

Abstract

This paper computes the Dirac cohomology HD(π) of irreducible unitary Harish-Chandra modules π 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 π contributing to HD(π). This confirms conjectures formulated by the first named author and Pandžić in 2011.