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

Alexander Braverman; Michael Finkelberg; David Kazhdan; Roman Travkin

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

Representation Theory 2026-03-11 v2 High Energy Physics - Theory Number Theory

Authors: Alexander Braverman , Michael Finkelberg , David Kazhdan , Roman Travkin

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.

Keywords

langlands correspondence

Cite

@article{arxiv.2412.20544,
  title  = {Relative Langlands duality for $\mathfrak{osp}(2n + 1|2n)$},
  author = {Alexander Braverman and Michael Finkelberg and David Kazhdan and Roman Travkin},
  journal= {arXiv preprint arXiv:2412.20544},
  year   = {2026}
}

Comments

v2: Lemma 3.5.2 added; the proofs of Lemmas 3.1.1, 3.4.2 and 3.5.3 corrected and expanded

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

Abstract

Keywords

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