The center of the wreath product of symmetric group algebras

O. Tout

doi:10.12958/adm1338

The center of the wreath product of symmetric group algebras

O. Tout^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	302-322
Number of pages	21
Journal	Algebra and Discrete Mathematics
Volume	31
Issue number	2
DOIs	https://doi.org/10.12958/adm1338
Publication status	Published - 2021

Keywords

Centers of finite groups algebras
Structure coefficients
Symmetric groups
Wreath products

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.12958/adm1338

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AB - 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.

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KW - Structure coefficients

KW - Symmetric groups

KW - Wreath products

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The center of the wreath product of symmetric group algebras

Abstract

Keywords

ASJC Scopus subject areas

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