A progenerator for representations of SL(n,q) in transverse characteristic

Details A progenerator for representations of SL(n,q) in transverse characteristic A progenerator for representations of SL(n,q) in transverse characteristic

2011-03-21

arxiv.org/abs/1103.4031v1

Mathematics

Representation Theory

4 pages

Scientific paper

Let G=GL(n,q), SL(n,q) or PGL(n,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 be the central primitive idempotent of the group algebra RD(U) corresponding to the projection on the invariant RD(U)-submodule. The aim of this note is to prove that the R-algebras RG and eRGe are Morita equivalent (through the natural functor sending an RG-module M to the eRGe-module eM).

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