Scattered representations of SL(n, ℂ)

Let $G$ be $S L (n, ℂ)$ . 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 $G$ .

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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

Vol. 309, No. 2, 2020

Chao-Ping Dong and Kayue Daniel Wong

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors