@article{cad47207e5ae4dd1a32e6ec04b9ab153,
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",
issn = "1726-3255",
publisher = "Institute of Applied Mathematics And Mechanics of the National Academy of Sciences of Ukraine",
number = "2",
}