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| Format: | Preprint |
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2020
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| Online Access: | https://arxiv.org/abs/2001.07584 |
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| _version_ | 1866917199904505856 |
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| author | Webster, Ben |
| author_facet | Webster, Ben |
| contents | In this paper, we consider the categorical symmetric Howe duality introduced by Khovanov, Lauda, Sussan and Yonezawa. While originally defined from a purely diagrammatic perspective, this construction also has geometric and representation-theoretic interpretations, corresponding to certain perverse sheaves on spaces of quiver representations and the category of Gelfand-Tsetlin modules over $\mathfrak{gl}_n$.
In particular, we show that the "deformed Webster algebras" discussed in work of Khovanov-Lauda-Sussan-Yonezawa manifest a Koszul duality between blocks of the category of Gelfand-Tsetlin modules over $\mathfrak{gl}_n$, and the constructible sheaves on representations of a linear quiver invariant under a certain parabolic in the group that acts by changing bases. Furthermore, we show that this duality intertwines translation functors with a diagrammatic categorical action. Includes an appendix by the author and Jerry Guan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_07584 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Three perspectives on categorical symmetric Howe duality Webster, Ben Representation Theory Algebraic Geometry In this paper, we consider the categorical symmetric Howe duality introduced by Khovanov, Lauda, Sussan and Yonezawa. While originally defined from a purely diagrammatic perspective, this construction also has geometric and representation-theoretic interpretations, corresponding to certain perverse sheaves on spaces of quiver representations and the category of Gelfand-Tsetlin modules over $\mathfrak{gl}_n$. In particular, we show that the "deformed Webster algebras" discussed in work of Khovanov-Lauda-Sussan-Yonezawa manifest a Koszul duality between blocks of the category of Gelfand-Tsetlin modules over $\mathfrak{gl}_n$, and the constructible sheaves on representations of a linear quiver invariant under a certain parabolic in the group that acts by changing bases. Furthermore, we show that this duality intertwines translation functors with a diagrammatic categorical action. Includes an appendix by the author and Jerry Guan. |
| title | Three perspectives on categorical symmetric Howe duality |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2001.07584 |