An algebraic approach to representations of the permutation group
General Mathematics
2007-05-23 v1 Group Theory
Abstract
The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group are a product of a Young symmetriser and a Young antisymmetriser. They form non-orthogonal bases of right and left modules. The non-orthogonality is compensated by a constant matrix. It turns out that this reduces the matrix entries to -1, 0,+1. An algorithm to compute the projectors is given.
Cite
@article{arxiv.math/0112117,
title = {An algebraic approach to representations of the permutation group},
author = {G. Bergdolt},
journal= {arXiv preprint arXiv:math/0112117},
year = {2007}
}