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Gelfand Pairs Involving the Wreath Product of Finite Abelian Groups with Symmetric Groups
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 64 / Issue 1 / March 2021
- Published online by Cambridge University Press:
- 13 April 2020, pp. 91-97
- Print publication:
- March 2021
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- Article
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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.
