Computing Green functions in small characteristic

JOURNAL OF ALGEBRA

卷:561

Article

Geck, Meinolf¹ 

[1] Univ Stuttgart, IAZ Lehrstuhl Algebra, Paffenwaldring 57, D-70569 Stuttgart, Germany

关键词: Finite groups of Lie type;    Green functions;    Character sheaves;   

DOI  :  10.1016/j.jalgebra.2019.12.016

来源: Elsevier

【 摘 要 】

Let G(q) be a finite group of Lie type over a field with q elements, where q is a prime power. The Green functions of G(q), as defined by Deligne and Lusztig, are known in almost all cases by work of Beynon-Spaltenstein, Lusztig and Shoji. Open cases exist for groups of exceptional type E-2(6), E-7, E-8 in small characteristics. We propose a general method for dealing with these cases, which proceeds by a reduction to the case where q is a prime and then uses computer algebra techniques. In this way, all open cases in type E-2(6), E-7 are solved, as well as at least one particular open case in type E-8. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free