Complements on disconnected reductive groups

François Digne and Jean Michel

Vol. 279 (2015), No. 1-2, 203–228

DOI: 10.2140/pjm.2015.279.203

Abstract

We present several results on disconnected reductive groups, in particular, on the characteristic-zero representation theory of finite groups of Lie type coming from disconnected reductive groups in positive characteristic. We generalize slightly the setting of our 1994 paper on that subject and show how most of our earlier results extend to the new situation. In particular, we give a classification of quasi-semisimple conjugacy classes over an arbitrary algebraically closed field, and over finite fields; we generalize a formula of Steinberg on the number of unipotent classes to disconnected groups and a formula for the tensor product of the Steinberg character with a Lusztig induced character.

Dedicated to the memory of Robert Steinberg

Keywords

nonconnected reductive groups

Mathematical Subject Classification 2010

Primary: 20G15

Secondary: 20G40, 20C33, 20G05

Milestones

Received: 3 March 2015

Revised: 5 March 2015

Accepted: 5 March 2015

Published: 21 December 2015