Vol. 309, No. 2, 2020

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

Chao-Ping Dong and Kayue Daniel Wong

Vol. 309 (2020), No. 2, 289–312
Abstract

Let $G$ be $SL\left(n,ℂ\right)$. The unitary dual $\stackrel{̂}{G}$ 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 ${\stackrel{̂}{G}}^{d}$—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
Primary: 22E46
Secondary: 17B56
Milestones
Received: 23 October 2019
Revised: 19 September 2020
Accepted: 22 September 2020
Published: 14 January 2021
Authors
 Chao-Ping Dong School of Mathematical Sciences Soochow University Suzhou China Kayue Daniel Wong School of Science and Engineering The Chinese University of Hong Kong, Shenzhen Shenzhen China