Quantum wreath products and Schur--Weyl duality II
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910259503693824 |
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| author | Lai, Chun-Ju Nakano, Daniel K. Xiang, Ziqing |
| author_facet | Lai, Chun-Ju Nakano, Daniel K. Xiang, Ziqing |
| contents | In the first part of this series, the authors introduced the quantum wreath product, providing a unified framework that encompasses numerous results previously addressed only through case-by-case analysis. This paper shifts focus to the fundamental construction of modules over these products, termed wreath modules. Our approach utilizes parabolic induction on tensor products combined with a sophisticated labeling scheme based on multipartitions. While the underlying constructions are technically involved, they offer a transparent realization of several prominent module families. Specifically, these wreath modules recover and unify: Simple modules over the Ariki-Koike algebra; Specht and simple modules over the Hu algebra; (anti)spherical modules and Kashiwara-Miwa-Stern modules over the affine Hecke algebra and its pro-p Iwahori variants. Finally, we demonstrate that these wreath modules for the Hu algebra serve as a critical component in solving the Ginzburg-Guay-Opdam-Rouquier problem. This solution enables a concrete realization of Category O for the rational Cherednik algebra in Type D. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19825 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum wreath products and Schur--Weyl duality II Lai, Chun-Ju Nakano, Daniel K. Xiang, Ziqing Representation Theory Quantum Algebra In the first part of this series, the authors introduced the quantum wreath product, providing a unified framework that encompasses numerous results previously addressed only through case-by-case analysis. This paper shifts focus to the fundamental construction of modules over these products, termed wreath modules. Our approach utilizes parabolic induction on tensor products combined with a sophisticated labeling scheme based on multipartitions. While the underlying constructions are technically involved, they offer a transparent realization of several prominent module families. Specifically, these wreath modules recover and unify: Simple modules over the Ariki-Koike algebra; Specht and simple modules over the Hu algebra; (anti)spherical modules and Kashiwara-Miwa-Stern modules over the affine Hecke algebra and its pro-p Iwahori variants. Finally, we demonstrate that these wreath modules for the Hu algebra serve as a critical component in solving the Ginzburg-Guay-Opdam-Rouquier problem. This solution enables a concrete realization of Category O for the rational Cherednik algebra in Type D. |
| title | Quantum wreath products and Schur--Weyl duality II |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2511.19825 |