Twists of rational Cherednik algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912184485806080 |
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| author | Bazlov, Yuri Berenstein, Arkady Jones-Healey, Edward McGaw, Alexander |
| author_facet | Bazlov, Yuri Berenstein, Arkady Jones-Healey, Edward McGaw, Alexander |
| contents | We show that braided Cherednik algebras introduced by the first two authors are cocycle twists of rational Cherednik algebras of the imprimitive complex reflection groups $G(m,p,n)$, when $m$ is even. This gives a new construction of mystic reflection groups which have Artin-Schelter regular rings of quantum polynomial invariants. As an application of this result, we show that a braided Cherednik algebra has a finite-dimensional representation if and only if its rational counterpart has one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11971 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Twists of rational Cherednik algebras Bazlov, Yuri Berenstein, Arkady Jones-Healey, Edward McGaw, Alexander Quantum Algebra Representation Theory 16T99 (Primary) 16G99, 20F55 (Secondary) We show that braided Cherednik algebras introduced by the first two authors are cocycle twists of rational Cherednik algebras of the imprimitive complex reflection groups $G(m,p,n)$, when $m$ is even. This gives a new construction of mystic reflection groups which have Artin-Schelter regular rings of quantum polynomial invariants. As an application of this result, we show that a braided Cherednik algebra has a finite-dimensional representation if and only if its rational counterpart has one. |
| title | Twists of rational Cherednik algebras |
| topic | Quantum Algebra Representation Theory 16T99 (Primary) 16G99, 20F55 (Secondary) |
| url | https://arxiv.org/abs/2205.11971 |