Relative Langlands duality for $\mathfrak{osp}(2n + 1|2n)$

Alexander Braverman; Michael Finkelberg; David Kazhdan; Roman Travkin

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arXiv · 2412.20544

Relative Langlands duality for $\mathfrak{osp}(2n + 1|2n)$

Alexander Braverman·Michael Finkelberg·David Kazhdan·Roman Travkin

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Abstract

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.

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Alexander Braverman, Michael Finkelberg, David Kazhdan, Roman Travkin. 2026-03-10. Relative Langlands duality for $\mathfrak{osp}(2n + 1|2n)$. https://arxiv.org/abs/2412.20544

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