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Some Singular Examples of Relative Langlands Duality
Published 28 May 2024 in math.NT and math.AG | (2405.18212v1)
Abstract: 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.
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