论文标题
Gelfand对涉及有限阿贝尔组的花环产物与对称组
Gelfand pairs involving the wreath product of finite abelian groups with symmetric groups
论文作者
论文摘要
众所周知，这对$（\ Mathcal {s} _n，\ Mathcal {s} _ {n-1}）$是$ n $元素上的对称组。在本文中，我们证明，如果$ g $是有限的组，则$（g \ wr \ nathcal {s} _n，g \ wr \ nathcal {s} _ {n-1}），$ $ g \ wr \ wr \ mathcal {s} _n $仅是$ g $ by $ g $ a $ gelf $ gelf $ gell i if $ i i ifcal ifcal ifcal ifcal ifcal ifcal if}如果$ G $是Abelian。
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.
