Super duality for Whittaker modules and finite $W$-algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918275882942464 |
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| author | Cheng, Shun-Jen Wang, Weiqiang |
| author_facet | Cheng, Shun-Jen Wang, Weiqiang |
| contents | We establish a super duality as an equivalence between Whittaker module categories over a pair of classical Lie algebra and Lie superalgebra in the infinite-rank limit. Building on this result and utilizing the Losev-Shu-Xiao decomposition, we obtain a super duality which is an equivalence between module categories over a pair of finite $W$-algebras and $W$-superalgebras at the infinite-rank limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08617 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Super duality for Whittaker modules and finite $W$-algebras Cheng, Shun-Jen Wang, Weiqiang Representation Theory 17B10, 17B20 We establish a super duality as an equivalence between Whittaker module categories over a pair of classical Lie algebra and Lie superalgebra in the infinite-rank limit. Building on this result and utilizing the Losev-Shu-Xiao decomposition, we obtain a super duality which is an equivalence between module categories over a pair of finite $W$-algebras and $W$-superalgebras at the infinite-rank limit. |
| title | Super duality for Whittaker modules and finite $W$-algebras |
| topic | Representation Theory 17B10, 17B20 |
| url | https://arxiv.org/abs/2410.08617 |