Automizers as extended reflection groups
Group Theory
2010-10-22 v1 Representation Theory
Abstract
Brou\'e, Malle and Michel have shown that the automizer of an abelian Sylow p-subgroup in a finite simple Chevalley group is an irreducible complex reflection group, for p not too small and different from the defining characteristic. The aim is this note is to show that a suitable version of this property holds for general finite groups. As an example, the automizer of an 11-Sylow subgroup in the Monster is the 2-dimensional complex reflection group G_{16}.
Cite
@article{arxiv.1010.4340,
title = {Automizers as extended reflection groups},
author = {Raphaël Rouquier},
journal= {arXiv preprint arXiv:1010.4340},
year = {2010}
}