Gelfand Pairs Involving the Wreath Product of Finite Abelian Groups with Symmetric Groups
Keyword(s):
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.
1979 ◽
Vol 20
(1)
◽
pp. 57-70
◽
Keyword(s):
1969 ◽
Vol 21
◽
pp. 684-701
◽
Keyword(s):
1982 ◽
Vol 33
(1)
◽
pp. 76-85
Keyword(s):
2017 ◽
Vol 16
(02)
◽
pp. 1750025
◽
Keyword(s):
2017 ◽
Vol 16
(04)
◽
pp. 1750065
◽
Keyword(s):
1976 ◽
Vol 79
(3)
◽
pp. 433-441
Keyword(s):
2013 ◽
Vol 88
(3)
◽
pp. 448-452
◽
Keyword(s):
2008 ◽
Vol 51
(2)
◽
pp. 273-284
◽
Keyword(s):
2015 ◽
Vol 08
(04)
◽
pp. 1550070
◽
Keyword(s):