A short note on Howlett-Lehrer theory

This paper gives two results which add to the structure theory of the endomorphism ring of an induced cuspidal module in non-describing characteristic. The first is that the presentation of the endomorphism ring in non-describing characteristic is really the same as the one given by Howlett and Lehrer for characteristic 0. This improves a result of Geck, Hiss and Malle. Inductions from conjugate Levi subgroups are equivalent as functors. Therefore the endomorphism rings are isomorphic by a natural map. The second result gives a condition, in which cases this map also preserves the presentation of the endomorphism ring from above.