Gelfand Pairs Involving the Wreath Product of Finite Abelian Groups with Symmetric Groups
Canadian mathematical bulletin, Tome 64 (2021) no. 1, pp. 91-97
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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.
Mots-clés :
Gelfand pairs, representation theory of finite groups, wreath product of finite abelian groups with symmetric groups
Tout, Omar. Gelfand Pairs Involving the Wreath Product of Finite Abelian Groups with Symmetric Groups. Canadian mathematical bulletin, Tome 64 (2021) no. 1, pp. 91-97. doi: 10.4153/S0008439520000259
@article{10_4153_S0008439520000259,
author = {Tout, Omar},
title = {Gelfand {Pairs} {Involving} the {Wreath} {Product} of {Finite} {Abelian} {Groups} with {Symmetric} {Groups}},
journal = {Canadian mathematical bulletin},
pages = {91--97},
year = {2021},
volume = {64},
number = {1},
doi = {10.4153/S0008439520000259},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000259/}
}
TY - JOUR AU - Tout, Omar TI - Gelfand Pairs Involving the Wreath Product of Finite Abelian Groups with Symmetric Groups JO - Canadian mathematical bulletin PY - 2021 SP - 91 EP - 97 VL - 64 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000259/ DO - 10.4153/S0008439520000259 ID - 10_4153_S0008439520000259 ER -
%0 Journal Article %A Tout, Omar %T Gelfand Pairs Involving the Wreath Product of Finite Abelian Groups with Symmetric Groups %J Canadian mathematical bulletin %D 2021 %P 91-97 %V 64 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000259/ %R 10.4153/S0008439520000259 %F 10_4153_S0008439520000259
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