Multiplicity-free representations of symmetric groups

2009/03/16 by Mark Wildon, Wildon, Mark
Mathematics · #20C20 #20C30 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Representation Theory (math.RT) #math.RT #msc:20C20 #msc:20C30

paper · pdf · doi:10.48550/arxiv.0903.2864

23 pages, 4 figures

arxiv created 2009/03/16 · openalex publication_date 2009/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Building on work of Saxl, we classify the multiplicity-free permutation characters of all symmetric groups of degree 66 or more. A corollary is a complete list of the irreducible characters of symmetric groups (again of degree 66 or more) which may appear in a multiplicity-free permutation representation. The multiplicity-free characters in a related family of monomial characters are also classified. We end by investigating a consequence of these results for Specht filtrations of permutation modules defined over fields of prime characteristic. Remark: parallel work of Godsil and Meagher (arXiv:math/0612567) gives an independent classification of the multiplicity-free permutation characters of symmetric groups of all degrees.

Citations

• Multiplicity-free representations of the symmetric group

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