Simple $B_4$ representations associated to cyclotomic Hecke algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918158607056896 |
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| author | Martirosyan, Lilit Wenzl, Hans |
| author_facet | Martirosyan, Lilit Wenzl, Hans |
| contents | We determine the structure of the cyclotomic Hecke algebra corresponding to the complex reflection group $G_{25}$ also when it is not semisimple, as long as the generators are diagonalizable. In particular, we classify all simple representations of the braid group $B_4$ for which the generators are diagonalizable and satisfy a cubic polynomial. This will be used in the classification of braided tensor categories of type $G_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple $B_4$ representations associated to cyclotomic Hecke algebras Martirosyan, Lilit Wenzl, Hans Representation Theory Category Theory Quantum Algebra We determine the structure of the cyclotomic Hecke algebra corresponding to the complex reflection group $G_{25}$ also when it is not semisimple, as long as the generators are diagonalizable. In particular, we classify all simple representations of the braid group $B_4$ for which the generators are diagonalizable and satisfy a cubic polynomial. This will be used in the classification of braided tensor categories of type $G_2$. |
| title | Simple $B_4$ representations associated to cyclotomic Hecke algebras |
| topic | Representation Theory Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2510.09928 |