Modular irreducibility of cuspidal unipotent characters
arXiv:1611.07373
Abstract
We prove a long-standing conjecture of Geck which predicts that cuspidal unipotent characters remain irreducible after -reduction. To this end, we construct a progenerator for the category of representations of a finite reductive group coming from generalised Gelfand--Graev representations. This is achieved by showing that cuspidal representations appear in the head of generalised Gelfand--Graev representations attached to cuspidal unipotent classes, as defined and studied in \cite{GM96}.
Version 2: Added a proof of Geck's conjecture, changed the title