Orbit method for p-Sylow subgroups of finite classical groups

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:223

Article

Guo, Qiong¹  Jedlitschky, Markus²  Dipper, Richard² 

[1] Shanghai Inst Technol, Coll Sci, Shanghai 201418, Peoples R China

[2] Univ Stuttgart, Inst Algebra & Zahlentheorie, D-70569 Stuttgart, Germany

关键词: p-Sylow subgroups;    Monomial linearisation;    Supercharacter;   

DOI  :  10.1016/j.jpaa.2019.02.016

来源: Elsevier

【 摘 要 】

For the p-Sylow subgroups U of the finite classical groups of untwisted Lie type, p an odd prime, we construct a monomial CU-module M which is isomorphic to the regular representation of CU by a modification of Kirillov's orbit method called monomial linearisation. We classify a certain subclass of orbits of the U-action on the monomial basis of M consisting of so called staircase orbits and show, that every orbit module in M is isomorphic to a staircase one. Finally we decompose the Andre-Neto supercharacters of U into a sum of U-characters afforded by staircase orbit modules contained in M. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free