Splitting Permutation Representations of Finite Groups by Polynomial Algebra Methods

Abstract

An algorithm for splitting permutation representations of a finite group over fields of characteristic zero into irreducible components is described. The algorithm is based on the fact that the components of the invariant inner product in invariant subspaces are operators of projection into these subspaces. An important part of the algorithm is the solution of systems of quadratic equations. A preliminary implementation of the algorithm splits representations up to dimensions of hundreds of thousands. Examples of computations are given in the appendix.