2024/12/29 by Alexander Braverman, Michael Finkelberg, Braverman, Alexander +5
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Physics Problems #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2412.20544
openalex publication_date 2024/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 SO(2n+1)× Sp(2n) acting on the tensor product of their tautological representations is the symplectic mirabolic space Sp(2n)\timesSp(2n) acting on the product T^* Sp(2n) and the tautological representations of Sp(2n). (Note that due to the anomaly, the dual of the second factor Sp(2n) is the metaplectic dual, i.e. Sp(2n)). We also formulate the corresponding global conjecture, which describes explicitly the categorical theta-correspondence on the Langlands dual side.