Scattered representations of complex classical Lie groups

Abstract

This paper studies scattered representations of $G=SO(2n+1,\mathbb{C})$, $Sp(2n,\mathbb{C})$ and $SO(2n,\mathbb{C})$, which lies in the `core' of the unitary spectrum $G$ with nonzero Dirac cohomology. We describe the Zhelobenko parameters of these representations, count their cardinality, and determine their spin-lowest $K$-types. We also disprove a conjecture raised in 2015 asserting that the unitary dual can be obtained via parabolic induction from irreducible unitary representations with non-zero Dirac cohomology.

20 pages, to appear in Int. Math. Res. Not. IMRN