Lifting representations of finite reductive groups: a character relation

Adler, Jeffrey D.; Cassel, Michael; Lansky, Joshua M.; Morgan, Emma; Zhao, Yifei

doi:10.2140/involve.2016.9.805

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1944-4184 (e-only)

ISSN: 1944-4176 (print)

Author Index

Coming Soon

Other MSP Journals

Lifting representations of finite reductive groups: a character relation

Jeffrey D. Adler, Michael Cassel, Joshua M. Lansky, Emma Morgan and Yifei Zhao

Vol. 9 (2016), No. 5, 805–812

DOI: 10.2140/involve.2016.9.805

Abstract

Given a connected reductive group $\tilde{G}$ over a finite field $k$ , and a semisimple $k$ -automorphism $ε$ of $\tilde{G}$ of finite order, let $G$ denote the connected part of the group of $ε$ -fixed points. Two of the authors have previously shown that there exists a natural lifting from series of representations of $G (k)$ to series for $\tilde{G} (k)$ . In the case of Deligne–Lusztig representations, we show that this lifting satisfies a character relation analogous to that of Shintani.

Keywords

finite reductive groups, Deligne–Lusztig representations, liftings, character relations

Mathematical Subject Classification 2010

Primary: 20C33

Secondary: 20G40

Milestones

Received: 27 May 2015

Revised: 1 November 2015

Accepted: 3 November 2015

Published: 25 August 2016

Communicated by Ken Ono

Authors

Jeffrey D. Adler
Department of Mathematics and Statistics American University Washington, DC 20016 %-8050 United States

Michael Cassel
Columbia University New York, NY 10027 %-7297 United States

Joshua M. Lansky
Department of Mathematics and Statistics American University Washington, DC 20016 %-8050 United States

Emma Morgan
Office of Institutional Research and Evaluation Tufts University Medford, MA 02155 United States

Yifei Zhao
Department of Mathematics Harvard University Cambridge, MA 02138 United States

Vol. 9, No. 5, 2016