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

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.

finite reductive groups, Deligne–Lusztig representations, liftings, character relations
Mathematical Subject Classification 2010
Primary: 20C33
Secondary: 20G40
Received: 27 May 2015
Revised: 1 November 2015
Accepted: 3 November 2015
Published: 25 August 2016

Communicated by Ken Ono
Jeffrey D. Adler
Department of Mathematics and Statistics
American University
Washington, DC 20016
United States
Michael Cassel
Columbia University
New York, NY 10027
United States
Joshua M. Lansky
Department of Mathematics and Statistics
American University
Washington, DC 20016
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