Scattered Representations of Complex Classical Lie Groups

Abstract

Abstract As a continuation of [9], this paper studies scattered representations of $SO(2n+1, {{\mathbb{C}}})$, $Sp(2n, {{\mathbb{C}}})$, and $SO(2n, {{\mathbb{C}}})$. 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 nonzero Dirac cohomology.