Simple periodic modules of twisted Chevalley groups

Peter Fleischmann and Jens Carsten Jantzen

Vol. 143 (1990), No. 2, 229–242

DOI: 10.2140/pjm.1990.143.229

Abstract

Consider a finite twisted Chevalley group constructed over a field of prime characteristic and its representations over an algebraically closed field of the same characteristic. In this paper we classify all those irreducible representations that are periodic, i.e., that have a periodic projective resolution. There is always the Steinberg module that is both simple and projective. We show that there are further periodic simple modules only for groups of types ²A₂ and ²B₂.

Mathematical Subject Classification 2000

Primary: 20G05

Secondary: 20C20, 20G40

Milestones

Received: 25 July 1988

Published: 1 June 1990