Scattered representations of $SL(n,\mathbb{C})$

Chao-Ping Dong and Kayue Daniel Wong

Vol. 309 (2020), No. 2, 289–312

DOI: 10.2140/pjm.2020.309.289

Abstract

Let $G$ be $SL\left(n,ℂ\right)$. The unitary dual $\hat{G}$ was classified by Vogan in the 1980s. This paper aims to describe the Zhelobenko parameters and the spin-lowest $K$-types of the scattered representations of $G$, which lie at the heart of ${\hat{G}}^d$—the set of all the equivalence classes of irreducible unitary representations of $G$ with nonvanishing Dirac cohomology. As a consequence, we will verify a couple of conjectures of Dong for $G$.

Keywords

Dirac cohomology, unitary representations, scattered representations

Mathematical Subject Classification 2010

Primary: 22E46

Secondary: 17B56

Milestones

Received: 23 October 2019

Revised: 19 September 2020

Accepted: 22 September 2020

Published: 14 January 2021