Multiplicity-free representations of symmetric groups

Mark Wildon

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arXiv · 0903.2864

Multiplicity-free representations of symmetric groups

Mark Wildon

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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.

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Mark Wildon. 2009-03-16. Multiplicity-free representations of symmetric groups. https://arxiv.org/abs/0903.2864

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