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(n, ). The unitary dual Ĝ 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 Ĝd—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
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