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Gelfand Pairs Involving the Wreath Product of Finite Abelian Groups with Symmetric Groups
Published online by Cambridge University Press: 13 April 2020
Abstract
It is well known that the pair 
$(\mathcal {S}_n,\mathcal {S}_{n-1})$ is a Gelfand pair where 
$\mathcal {S}_n$ is the symmetric group on n elements. In this paper, we prove that if G is a finite group then 
$(G\wr \mathcal {S}_n, G\wr \mathcal {S}_{n-1}),$ where 
$G\wr \mathcal {S}_n$ is the wreath product of G by 
$\mathcal {S}_n,$ is a Gelfand pair if and only if G is abelian.
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