On imprimitive representations of finite reductive groups in non-defining characteristic

JOURNAL OF ALGEBRA

卷:556

Article

Klupsch, Matthias¹ 

[1] Rhein Westfal TH Aachen, Lehrstuhl Math D, Pontdriesch 14-16, D-52062 Aachen, Germany

关键词: Modular representation theory;    Finite reductive groups;    Harish-Chandra induction;    Imprimitive representation;   

DOI  :  10.1016/j.jalgebra.2020.03.016

来源: Elsevier

【 摘 要 】

In this paper, we begin with the classification of Harish-Chandra imprimitive representations in non-defining characteristic. We recall the connection of this problem to certain generalizations of Iwahori-Hecke algebras and show that Harish-Chandra induction is compatible with the Morita equivalence by Bonnafe and Rouquier, thus reducing the classification problem to quasi-isolated blocks. Afterwards, we consider imprimitivity of unipotent representations of certain classical groups. In the case of general linear and unitary groups, our reduction methods then lead to results for arbitrary Lusztig series. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free