Schurification of polynomial quantum wreath products
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910274261352448 |
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| author | Lai, Chun-Ju Minets, Alexandre |
| author_facet | Lai, Chun-Ju Minets, Alexandre |
| contents | We study the Schur algebra counterpart of a vast class of quantum wreath products. This is achieved by developing a theory of twisted convolution algebras, inspired by geometric intuition. In parallel, we provide an algebraic Schurification via a Kashiwara-Miwa-Stern-type action on a tensor space. We give a uniform proof of Schur duality, and construct explicit bases of the new Schur algebras. This provides new results for, among other examples, Vignéras' pro-$p$ Iwahori Hecke algebras of type $A$, degenerate affine Hecke algebras, Kleshchev-Muth's affine zigzag algebras, and Rosso-Savage's affine Frobenius Hecke algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schurification of polynomial quantum wreath products Lai, Chun-Ju Minets, Alexandre Representation Theory Quantum Algebra 20C08, 20G43, 17B37 We study the Schur algebra counterpart of a vast class of quantum wreath products. This is achieved by developing a theory of twisted convolution algebras, inspired by geometric intuition. In parallel, we provide an algebraic Schurification via a Kashiwara-Miwa-Stern-type action on a tensor space. We give a uniform proof of Schur duality, and construct explicit bases of the new Schur algebras. This provides new results for, among other examples, Vignéras' pro-$p$ Iwahori Hecke algebras of type $A$, degenerate affine Hecke algebras, Kleshchev-Muth's affine zigzag algebras, and Rosso-Savage's affine Frobenius Hecke algebras. |
| title | Schurification of polynomial quantum wreath products |
| topic | Representation Theory Quantum Algebra 20C08, 20G43, 17B37 |
| url | https://arxiv.org/abs/2502.02108 |