Geometrizations of quantum groups and dual semicanonical bases
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913329774067712 |
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| author | Bi, Yingjin |
| author_facet | Bi, Yingjin |
| contents | In this paper, we give a geometrization of semicanonical bases of quantum groups via Grothendieck groups of the derived categories of Lusztig's nilpotent varieties. Meanwhile, we describe the dual semicanonical bases in terms of Serre polynomials of Grassmannians of modules over preprojective algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00663 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometrizations of quantum groups and dual semicanonical bases Bi, Yingjin Representation Theory Algebraic Geometry Quantum Algebra Rings and Algebras 17B37, 16G20, 20G42 In this paper, we give a geometrization of semicanonical bases of quantum groups via Grothendieck groups of the derived categories of Lusztig's nilpotent varieties. Meanwhile, we describe the dual semicanonical bases in terms of Serre polynomials of Grassmannians of modules over preprojective algebras. |
| title | Geometrizations of quantum groups and dual semicanonical bases |
| topic | Representation Theory Algebraic Geometry Quantum Algebra Rings and Algebras 17B37, 16G20, 20G42 |
| url | https://arxiv.org/abs/2404.00663 |