Gelfand Pairs Involving the Wreath Product of Finite Abelian Groups with Symmetric Groups. Issue 1 (13th March 2021)

• Record Type: Journal Article
• Authors: Tout, Omar
• Is Part Of: Canadian mathematical bulletin =. Volume 64:Issue 1(2021)
• Page Start: 91
• Page End: 97
• Publication Date: 2021-03-13
• Subjects: 05E10, -- 20C30; Gelfand pairs, -- representation theory of finite groups, -- wreath product of finite abelian groups with symmetric groups; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/S0008439520000259
• Languages: English
• ISSNs: 0008-4395

Abstract

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.