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Some Singular Examples of Relative Langlands Duality

Number Theory 2024-05-29 v1 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.2405.18212,
  title  = {Some Singular Examples of Relative Langlands Duality},
  author = {Eric Y. Chen and Akshay Venkatesh},
  journal= {arXiv preprint arXiv:2405.18212},
  year   = {2024}
}
R2 v1 2026-06-28T16:43:54.758Z