On cuspidal and supercuspidal representations of finite reductive groups

• Über kuspidale und superkuspidale Darstellungen endlicher reduktiver Gruppen

Klupsch, Matthias; Hiß, Gerhard (Thesis advisor); Geck, Meinolf (Thesis advisor); Nebe, Gabriele (Thesis advisor)

Aachen (2016)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2016

Abstract

This thesis is about the modular representation theory of finite reductive groups in non-defining characteristic and, in particular, about the development of methods which lead to a better understanding of cuspidal and especially supercuspidal representations of these groups. By a conjecture by Gerhard Hiss, every irreducible supercuspidal representation lifts to a representation in characteristic 0. An even stronger conjecture by Meinolf Geck states that the reductions modulo l of certaincuspidal irreducible representations are also irreducible. An important part of this thesis is the reduction of these two conjectures to the case where the algebraic group to be considered is simple.