Abstract:
We consider the wreath product of two symmetric groups as a group of blocks permutations and we study its conjugacy classes. We give a polynomiality property for the structure coefficients of the center of the wreath product of symmetric group algebras. This allows us to recover an old result of Farahat and Higman about the polynomiality of the structure coefficients of the center of the symmetric group algebra and to generalize our recent result about the polynomiality property of the structure coefficients of the center of the hyperoctahedral group algebra.
Keywords:
symmetric groups, wreath products, structure coefficients, centers of finite groups algebras.
\Bibitem{Tou21}
\by O.~Tout
\paper The center of the wreath product of symmetric group algebras
\jour Algebra Discrete Math.
\yr 2021
\vol 31
\issue 2
\pages 302--322
\mathnet{http://mi.mathnet.ru/adm802}
\crossref{https://doi.org/10.12958/adm1338}
Linking options:
https://www.mathnet.ru/eng/adm802
https://www.mathnet.ru/eng/adm/v31/i2/p302
This publication is cited in the following 1 articles:
Omar Tout, “THE ALGEBRA OF CONJUGACY CLASSES OF THE WREATH PRODUCT OF A FINITE GROUP WITH THE SYMMETRIC GROUP”, Rocky Mountain J. Math., 53:2 (2023)
Citation in format AMSBIB
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