Lusztig sheaves and tensor products of integrable highest weight modules
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916822764224512 |
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| author | Fang, Jiepeng Lan, Yixin |
| author_facet | Fang, Jiepeng Lan, Yixin |
| contents | By introducing $N$-framed quivers, we define the localization of Lusztig's sheaves for $N$-framed quivers and functors $E^{(n)}_{i}, F^{(n)}_{i}, K^{\pm}_i$ for localizations. This gives a categorical realization of tensor products of integrable highest weight modules of the quantized enveloping algebra. The simple perverse sheaves in the localization provide a basis of the tensor product. We prove that this basis coincides with the canonical basis of tensor product in the sense of Lusztig and Bao-Wang. Moreover, we give a categorical interpretation of the Yang-Baxter equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18682 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lusztig sheaves and tensor products of integrable highest weight modules Fang, Jiepeng Lan, Yixin Representation Theory Quantum Algebra 16G20, 17B37 By introducing $N$-framed quivers, we define the localization of Lusztig's sheaves for $N$-framed quivers and functors $E^{(n)}_{i}, F^{(n)}_{i}, K^{\pm}_i$ for localizations. This gives a categorical realization of tensor products of integrable highest weight modules of the quantized enveloping algebra. The simple perverse sheaves in the localization provide a basis of the tensor product. We prove that this basis coincides with the canonical basis of tensor product in the sense of Lusztig and Bao-Wang. Moreover, we give a categorical interpretation of the Yang-Baxter equation. |
| title | Lusztig sheaves and tensor products of integrable highest weight modules |
| topic | Representation Theory Quantum Algebra 16G20, 17B37 |
| url | https://arxiv.org/abs/2310.18682 |