Vol. 9, No. 5, 2016

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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
Abstract

Given a connected reductive group G˜ over a finite field k, and a semisimple k-automorphism ε of 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 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