An algebraic approach to representations of the permutation group

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.