Labelling the character tables of symmetric and alternating groups

2006/12/11 by Mark Wildon, Wildon, Mark
Chemistry · Mathematics · #20C20 #20C30 #FOS: Mathematics #History and advancements in chemistry #Representation Theory (math.RT) #math.RT #msc:20C20 #msc:20C30

paper · pdf · doi:10.48550/arxiv.math/0612292

12 pages

arxiv created 2006/12/11 · openalex publication_date 2006/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a character table of the symmetric group S_n. It is shown that unless n = 4 or n=6, there is a unique way to assign partitions of n to the rows and columns of X so that for all λ and ν, X_λν is equal to χ^λ(ν), the value of the irreducible character of S_n labelled by λ on elements of cycle type ν. Analogous results are proved for alternating groups, and for the Brauer character tables of symmetric and alternating groups.

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