On the relative Langlands duality for Sp_2n \backslash GL_2n+1 (with an appendix by Zeyu Wang)

2025/04/26 by Wenting Lu, Zeyu Wang, Lu, Weixiao +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2504.18774

Abstract

We verify the relative Langlands duality conjecture proposed by Ben-Zvi, Sakellaridis, Venkatesh for the hyperspherical Hamiltonian variety T^*(Sp_2n\backslash GL_2n+1). We provide numerical (over number fields and function fields) and geometric (in the étale setting) evidence that its dual Hamiltonian variety should be T^*(GL_n × GL_n+1 \backslash GL_2n+1) as is predicted by Ben-Zvi, Sakellaridis, Venkatesh.

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