Construction of the irreducible modular representations of a finite group

JOURNAL OF ALGEBRA

卷:545

Article

Cannon, John J.¹  Steel, Allan K.¹  Unger, William R.¹ 

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW, Australia

关键词: Representation theory;    Brauer characters;    Irreducible modules;    Finite groups;   

DOI  :  10.1016/j.jalgebra.2019.08.015

来源: Elsevier

【 摘 要 】

A complete procedure is described for constructing the irreducible KG-modules and their Brauer characters, where K is a finite field of characteristic p and G is a finite permutation or matrix group. The central idea is to construct a sequence {S-1,. . . ,S-n} of KG-modules, each having relatively small dimension, such that each S-i has one or more irreducible constituents that are not constituents of S-1,. . . ,Si-1 The Meataxe, used in conjunction with condensation, is used to extract the new irreducibles from each S-i. The algorithm has been implemented in MAGMA and is capable of constructing irreducibles of dimension over 200 000. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free