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

This paper computes the Dirac cohomology $H_D(π)$ 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 $H_D(π)$. This confirms conjectures formulated by the first named author and Pandzic in 2011.

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