Categories of Weight Modules for Unrolled Restricted Quantum Groups at Roots of Unity
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866914667169841152 |
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| author | Rupert, Matthew |
| author_facet | Rupert, Matthew |
| contents | Motivated by connections to the singlet vertex operator algebra in the $\mathfrak{g}=\mathfrak{sl}_2$ case, we study the unrolled restricted quantum groups $\overline{U}_q^H(\mathfrak{g})$ at arbitrary roots of unity with a focus on its category of weight modules. We show that the braid group action on the Drinfeld-Jimbo algebra $U_q(\mathfrak{g})$ naturally extends to the unrolled quantum groups and that the category of weight modules is a generically semi-simple ribbon category (previously known only for odd roots) with trivial Müger center. Projective covers of simple modules are shown to be self-dual, and some preliminary connections to the higher rank singlet vertex operator algebras are motivated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_05922 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Categories of Weight Modules for Unrolled Restricted Quantum Groups at Roots of Unity Rupert, Matthew Representation Theory Quantum Algebra 17B37 Motivated by connections to the singlet vertex operator algebra in the $\mathfrak{g}=\mathfrak{sl}_2$ case, we study the unrolled restricted quantum groups $\overline{U}_q^H(\mathfrak{g})$ at arbitrary roots of unity with a focus on its category of weight modules. We show that the braid group action on the Drinfeld-Jimbo algebra $U_q(\mathfrak{g})$ naturally extends to the unrolled quantum groups and that the category of weight modules is a generically semi-simple ribbon category (previously known only for odd roots) with trivial Müger center. Projective covers of simple modules are shown to be self-dual, and some preliminary connections to the higher rank singlet vertex operator algebras are motivated. |
| title | Categories of Weight Modules for Unrolled Restricted Quantum Groups at Roots of Unity |
| topic | Representation Theory Quantum Algebra 17B37 |
| url | https://arxiv.org/abs/1910.05922 |