An algebraic approach to representations of the permutation group

2001/12/12 by G. Bergdolt, Bergdolt, G.
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #General Mathematics (math.GM) #Group Theory (math.GR) #Wireless Communication Networks Research #graph theory and CDMA systems #math.GM #math.GR

paper · pdf · doi:10.48550/arxiv.math/0112117

arxiv created 2001/12/12 · openalex publication_date 2001/12/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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