Relative Langlands duality for $\mathfrak{osp}(2n + 1|2n)$
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917326292516864 |
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| author | Braverman, Alexander Finkelberg, Michael Kazhdan, David Travkin, Roman |
| author_facet | Braverman, Alexander Finkelberg, Michael Kazhdan, David Travkin, Roman |
| contents | We establish an $S$-duality converse to the one studied by the 1st, 2nd and 4th authors; this is also a case of a twisted version of the relative Langlands duality of Ben Zvi, Sakellaridis and Venkatesh.. Namely, we prove that the $S$-dual of $\text{SO}(2n+1)\times \text{Sp}(2n)$ acting on the tensor product of their tautological representations is the symplectic mirabolic space $\text{Sp}(2n)\times\text{Sp}(2n)$ acting on the product $T^* \text{Sp}(2n)$ and the tautological representations of $\text{Sp}(2n)$. (Note that due to the anomaly, the dual of the second factor $\text{Sp}(2n)$ is the metaplectic dual, i.e. $\text{Sp}(2n)$). We also formulate the corresponding global conjecture, which describes explicitly the categorical theta-correspondence on the Langlands dual side. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative Langlands duality for $\mathfrak{osp}(2n + 1|2n)$ Braverman, Alexander Finkelberg, Michael Kazhdan, David Travkin, Roman Representation Theory High Energy Physics - Theory Number Theory We establish an $S$-duality converse to the one studied by the 1st, 2nd and 4th authors; this is also a case of a twisted version of the relative Langlands duality of Ben Zvi, Sakellaridis and Venkatesh.. Namely, we prove that the $S$-dual of $\text{SO}(2n+1)\times \text{Sp}(2n)$ acting on the tensor product of their tautological representations is the symplectic mirabolic space $\text{Sp}(2n)\times\text{Sp}(2n)$ acting on the product $T^* \text{Sp}(2n)$ and the tautological representations of $\text{Sp}(2n)$. (Note that due to the anomaly, the dual of the second factor $\text{Sp}(2n)$ is the metaplectic dual, i.e. $\text{Sp}(2n)$). We also formulate the corresponding global conjecture, which describes explicitly the categorical theta-correspondence on the Langlands dual side. |
| title | Relative Langlands duality for $\mathfrak{osp}(2n + 1|2n)$ |
| topic | Representation Theory High Energy Physics - Theory Number Theory |
| url | https://arxiv.org/abs/2412.20544 |