The center of the wreath product of symmetric group algebras
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 Far...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2021 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188713 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The center of the wreath product of symmetric group algebras / O. Tout // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 2. — С. 302–322. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862664715073748992 |
|---|---|
| author | Tout, O. |
| author_facet | Tout, O. |
| citation_txt | The center of the wreath product of symmetric group algebras / O. Tout // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 2. — С. 302–322. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | 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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| first_indexed | 2025-12-07T15:15:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188713 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:15:00Z |
| publishDate | 2021 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Tout, O. 2023-03-11T16:20:08Z 2023-03-11T16:20:08Z 2021 The center of the wreath product of symmetric group algebras / O. Tout // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 2. — С. 302–322. — Бібліогр.: 12 назв. — англ. 1726-3255 DOI:10.12958/adm1338 2020 MSC: 05E10, 05E16, 20C30. https://nasplib.isofts.kiev.ua/handle/123456789/188713 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. This research is supported by Narodowe Centrum Nauki, grant number 2017/26/A/ST1/00189. 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics The center of the wreath product of symmetric group algebras Article published earlier |
| spellingShingle | The center of the wreath product of symmetric group algebras Tout, O. |
| title | The center of the wreath product of symmetric group algebras |
| title_full | The center of the wreath product of symmetric group algebras |
| title_fullStr | The center of the wreath product of symmetric group algebras |
| title_full_unstemmed | The center of the wreath product of symmetric group algebras |
| title_short | The center of the wreath product of symmetric group algebras |
| title_sort | center of the wreath product of symmetric group algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188713 |
| work_keys_str_mv | AT touto thecenterofthewreathproductofsymmetricgroupalgebras AT touto centerofthewreathproductofsymmetricgroupalgebras |