Testing modules for irreducibility

Journal of the Australian Mathematical Society

Derek F. Holt¹ 

[1] Sarah Rees

关键词: 20C40;    20-04;   

DOI  :  10.1017/S1446788700036016

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

A practical method is described for deciding whether or not a finite-dimensional module for a group over a finite field is reducible or not. In the reducible case, an explicit submodule is found. The method is a generalistaion of the Parker-Norton ‘Meataxe’ algorithm, but it does not depend for its efficiency on the field being small. The principal tools involved are the calculation of the nullspace and the characteristic polynomial of a matrix over a finite field, and the factorisation of the latter. Related algorithms to determine absolute irreducibility and module isomorphism for irreducibles are also described. Details of an implementation in the GAP system, together with some performance analyses are included.

【 授权许可】

Unknown