Selecta Mathematica· 2026Q1
Some singular examples of relative Langlands duality
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- 2026year
Short summary
This paper examines relative Langlands duality for singular spaces, specifically the nilpotent cones of 3x3 matrices and (2,2,2)-tensors, relating them to Rankin-Selberg integrals.
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Key points
- Explores relative Langlands duality for singular spaces.
- Examines the nilpotent cone of 3x3 matrices.
- Investigates the nilpotent cone of (2,2,2)-tensors.
- Connects these spaces to Rankin-Selberg integrals.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract Relative Langlands duality structures the study of automorphic periods around a putative duality between certain G -spaces and $$\check{G}$$ G ˇ -spaces, where $$G, \check{G}$$ G , G ˇ are 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 $$3 \times 3$$ 3 × 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.
The authors' abstract, as published at the source. Selecta Mathematica, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics