Quantum wreath products and Schur–Weyl duality I
In this paper, the authors introduce a new notion called the quantum wreath product, which is the algebra $B \wr _Q \mathcal {H}(d)$ produced from a given algebra B, a positive integer d and a choice $Q=(R,S,\rho ,\sigma )$ of parameters. Important examples that arise from our construc...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001038/type/journal_article |
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| author | Chun-Ju Lai Daniel K. Nakano Ziqing Xiang |
| author_facet | Chun-Ju Lai Daniel K. Nakano Ziqing Xiang |
| author_sort | Chun-Ju Lai |
| collection | DOAJ |
| description | In this paper, the authors introduce a new notion called the quantum wreath product, which is the algebra
$B \wr _Q \mathcal {H}(d)$
produced from a given algebra B, a positive integer d and a choice
$Q=(R,S,\rho ,\sigma )$
of parameters. Important examples that arise from our construction include many variants of the Hecke algebras, such as the Ariki–Koike algebras, the affine Hecke algebras and their degenerate version, Wan–Wang’s wreath Hecke algebras, Rosso–Savage’s (affine) Frobenius Hecke algebras, Kleshchev–Muth’s affine zigzag algebras and the Hu algebra that quantizes the wreath product
$\Sigma _m \wr \Sigma _2$
between symmetric groups. |
| format | Article |
| id | doaj-art-bbec16b84beb45c4a4d6596e8fabb36a |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-bbec16b84beb45c4a4d6596e8fabb36a2024-11-26T08:01:12ZengCambridge University PressForum of Mathematics, Sigma2050-50942024-01-011210.1017/fms.2024.103Quantum wreath products and Schur–Weyl duality IChun-Ju Lai0https://orcid.org/0000-0001-8433-0653Daniel K. Nakano1Ziqing Xiang2Institute of Mathematics, Academia Sinica, Taipei, 106319, TaiwanDepartment of Mathematics, University of Georgia, Athens, GA 30602, USA; E-mail:Department of Mathematics and National Center For Applied Mathematics Shenzhen, Southern University of Science and Technology, Shenzhen, 518055, China; E-mail:In this paper, the authors introduce a new notion called the quantum wreath product, which is the algebra $B \wr _Q \mathcal {H}(d)$ produced from a given algebra B, a positive integer d and a choice $Q=(R,S,\rho ,\sigma )$ of parameters. Important examples that arise from our construction include many variants of the Hecke algebras, such as the Ariki–Koike algebras, the affine Hecke algebras and their degenerate version, Wan–Wang’s wreath Hecke algebras, Rosso–Savage’s (affine) Frobenius Hecke algebras, Kleshchev–Muth’s affine zigzag algebras and the Hu algebra that quantizes the wreath product $\Sigma _m \wr \Sigma _2$ between symmetric groups.https://www.cambridge.org/core/product/identifier/S2050509424001038/type/journal_article20C0820G43 |
| spellingShingle | Chun-Ju Lai Daniel K. Nakano Ziqing Xiang Quantum wreath products and Schur–Weyl duality I Forum of Mathematics, Sigma 20C08 20G43 |
| title | Quantum wreath products and Schur–Weyl duality I |
| title_full | Quantum wreath products and Schur–Weyl duality I |
| title_fullStr | Quantum wreath products and Schur–Weyl duality I |
| title_full_unstemmed | Quantum wreath products and Schur–Weyl duality I |
| title_short | Quantum wreath products and Schur–Weyl duality I |
| title_sort | quantum wreath products and schur weyl duality i |
| topic | 20C08 20G43 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001038/type/journal_article |
| work_keys_str_mv | AT chunjulai quantumwreathproductsandschurweyldualityi AT danielknakano quantumwreathproductsandschurweyldualityi AT ziqingxiang quantumwreathproductsandschurweyldualityi |