A progenerator for representations of [formula omitted] in transverse characteristic

Abstract

Let G = GL n ( F q ) , SL n ( F q ) or PGL n ( F q ) , where q is a power of some prime number p, let U denote a Sylow p-subgroup of G and let R be a commutative ring in which p is invertible. Let D ( U ) denote the derived subgroup of U and let e = 1 | D ( U ) | ∑ u ∈ D ( U ) u . The aim of this Note is to prove that the R-algebras RG and e R G e are Morita equivalent (through the natural functor RG-mod → e R G e -mod, M ↦ e M ).