BGG Reciprocity for Generalized Weight Modules of Unrolled Restricted Quantum Groups at Roots of Unity
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909094510592000 |
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| author | Rupert, Matthew |
| author_facet | Rupert, Matthew |
| contents | We consider the category of generalized weight modules over the unrolled restricted quantum group $\overline{U}_q^H(\mathfrak{g})$ of a finite-dimensional simple complex Lie algebra $\mathfrak{g}$ at root of unity q. Although this category does not admit projective modules, it is filtered by subcategories with enough projectives. We show that the projective modules in these subcategories satisfy a variant of BGG reciprocity and give a generators and relations description of the projective covers of irreducible modules when $\mathfrak{g}=\mathfrak{sl}_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | BGG Reciprocity for Generalized Weight Modules of Unrolled Restricted Quantum Groups at Roots of Unity Rupert, Matthew Quantum Algebra Representation Theory 17B37 (Primary) We consider the category of generalized weight modules over the unrolled restricted quantum group $\overline{U}_q^H(\mathfrak{g})$ of a finite-dimensional simple complex Lie algebra $\mathfrak{g}$ at root of unity q. Although this category does not admit projective modules, it is filtered by subcategories with enough projectives. We show that the projective modules in these subcategories satisfy a variant of BGG reciprocity and give a generators and relations description of the projective covers of irreducible modules when $\mathfrak{g}=\mathfrak{sl}_2$. |
| title | BGG Reciprocity for Generalized Weight Modules of Unrolled Restricted Quantum Groups at Roots of Unity |
| topic | Quantum Algebra Representation Theory 17B37 (Primary) |
| url | https://arxiv.org/abs/2402.03668 |