2024/05/28 by Eric Chen, Chen, Eric Y., Akshay Venkatesh +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2405.18212
openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Relative Langlands duality structures the study of automorphic periods around a putative duality between certain group actions of Langlands dual reductive groups. In this article, after giving a self-contained exposition of the relevant ingredients from relative Langlands duality, we examine this proposal for some interesting pairs of singular spaces: one pair arising from the cone of nilpotent (3 x 3)-matrices, and the other pair arising from the nilpotent cone of (2,2,2)-tensors. These relate, respectively, to Rankin--Selberg integrals discovered by Ginzburg and Garrett.