Modular irreducibility of cuspidal unipotent characters

2016/11/22 by Dudas, Olivier, Malle, Gunter · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Primary 20C33 #Representation Theory (math.RT) #Secondary 20C08

paper · doi:10.48550/arxiv.1611.07373

Abstract

We prove a long-standing conjecture of Geck which predicts that cuspidal unipotent characters remain irreducible after ℓ-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 \citeGM96.

Cited by

• Jacquet modules of Tate cohomology and base change lifting

Related

• Irreducibility and cuspidality
• Modular reduction of complex representations of finite reductive groups
• Irreducibility Criteria for Local and Global Representations
• Cuspidal ℓ-modular representations of p-adic classical groups
• Geck's Conjecture and the Generalized Gelfand-Graev Representations in Bad Characteristic