Modular irreducibility of cuspidal unipotent characters

• 成果类型: Article
• 署名作者: Dudas, Olivier; Malle, Gunter
• 署名单位: Universite Paris Cite; University of Kaiserslautern
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0753-1
• 发表日期: 2018
• 页码: 579-589
• 关键词: gelfand-graev representations; brauer characters; reductive groups; finite-field; support; sheaves

摘要

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 Geck and Malle (J Lond Math Soc 2(53):63-78, 1996).