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GELFAND PAIRS INVOLVING THE WREATH PRODUCT OF FINITE ABELIAN GROUPS WITH SYMMETRIC GROUPS
Canadian Mathematical Bulletin ( IF 0.5 ) Pub Date : 2020-04-13 , DOI: 10.4153/s0008439520000259
Omar Tout

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.

中文翻译:

涉及有限阿贝尔群和对称群的圈积的格尔芬德对

众所周知,$(\mathcal{S}_n,\mathcal{S}_{n-1})$ 对是 Gelfand 对,其中 $\mathcal{S}_n$ 是 $n$ 上的对称群元素。在本文中,我们证明如果 $G$ 是一个有限群,那么 $(G\wr \mathcal{S}_n, G\wr \mathcal{S}_{n-1}),$ 其中 $G\wr \mathcal{S}_n$ 是 $G$ 与 $\mathcal{S}_n 的花环积,$ 是 Gelfand 对当且仅当 $G$ 是阿贝尔。
更新日期:2020-04-13
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