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Some Singular Examples of Relative Langlands Duality

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arxiv 2405.18212 v1 pith:22X5B37T submitted 2024-05-28 math.NT math.AG

Eric Y. Chen , Akshay Venkatesh This is my paper · ORCID
classification math.NTmath.AG
keywords dualitylanglandsrelativearisingconenilpotentpairsingular
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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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Cited by 1 Pith paper

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  1. Langlands Duality and Invariant Differential Operators

    math.RT 2024-11 conditional novelty 4.0 of 10

    The paper connects invariant differential operators to Langlands duality by showing that Knapp-Stein duality in representation multiplets of SL(2n,R) mimics Langlands dual pairs.

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