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October 2020 Finite Gelfand pairs and cracking points of the symmetric groups
Faith Pearson, Anna Romanov, Dylan Soller
Rocky Mountain J. Math. 50(5): 1807-1812 (October 2020). DOI: 10.1216/rmj.2020.50.1807

Abstract

Let Γ be a finite group. Consider the wreath product Gn:=ΓnSn and the subgroup Kn:=Δn×SnGn, where Sn is the symmetric group and Δn is the diagonal subgroup of Γn. For certain values of n (which depend on the group Γ), the pair (Gn,Kn) is a Gelfand pair. It is not known for all finite groups which values of n result in Gelfand pairs. Building off the work of Benson–Ratcliff [4], we obtain a result which simplifies the computation of multiplicities of irreducible representations in certain tensor product representations, then apply this result to show that for Γ=Sk, k5, (Gn,Kn) is a Gelfand pair exactly when n=1,2.

Citation

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Faith Pearson. Anna Romanov. Dylan Soller. "Finite Gelfand pairs and cracking points of the symmetric groups." Rocky Mountain J. Math. 50 (5) 1807 - 1812, October 2020. https://doi.org/10.1216/rmj.2020.50.1807

Information

Received: 1 September 2019; Revised: 16 March 2020; Accepted: 22 March 2020; Published: October 2020
First available in Project Euclid: 5 November 2020

zbMATH: 07274837
MathSciNet: MR4170689
Digital Object Identifier: 10.1216/rmj.2020.50.1807

Subjects:
Primary: 20C15, 20C30
Secondary: 20E22

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 5 • October 2020
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