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.
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}
}