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

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
Externally published	Yes

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

Cite this

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title = "The center of the wreath product of symmetric group algebras",

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 = "Centers of finite groups algebras, Structure coefficients, Symmetric groups, Wreath products",

author = "O. Tout",

note = "Funding Information: The author is grateful to the Mathematical Institute of the Polish Academy of Sciences branch in Toru{\'n} for their hospitality and financial support during the time where this work was accomplished. Especially, he would like to thank Prof. Piotr {\'S}niady for many interesting discussions about the topics presented in this paper. Funding Information: ∗This research is supported by Narodowe Centrum Nauki, grant number 2017/26/A/ST1/00189. 2020 MSC: 05E10, 05E16, 20C30. Key words and phrases: symmetric groups, wreath products, structure coefficients, centers of finite groups algebras. Publisher Copyright: {\textcopyright} Algebra and Discrete Mathematics.",

year = "2021",

doi = "10.12958/adm1338",

language = "English",

volume = "31",

pages = "302--322",

journal = "Algebra and Discrete Mathematics",

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publisher = "Institute of Applied Mathematics And Mechanics of the National Academy of Sciences of Ukraine",

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AU - Tout, O.

N1 - Funding Information: The author is grateful to the Mathematical Institute of the Polish Academy of Sciences branch in Toruń for their hospitality and financial support during the time where this work was accomplished. Especially, he would like to thank Prof. Piotr Śniady for many interesting discussions about the topics presented in this paper. Funding Information: ∗This research is supported by Narodowe Centrum Nauki, grant number 2017/26/A/ST1/00189. 2020 MSC: 05E10, 05E16, 20C30. Key words and phrases: symmetric groups, wreath products, structure coefficients, centers of finite groups algebras. Publisher Copyright: © Algebra and Discrete Mathematics.

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N2 - 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.

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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The center of the wreath product of symmetric group algebras

Abstract

Keywords

ASJC Scopus subject areas

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