On a tamely ramified local relative Langlands conjecture via categorical representations

2025/10/29 by Lin, Milton, Pham, Toan, Yu, Jize
#22E57 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.25231

Abstract

Let G be a complex reductive group. For a smooth affine spherical G-variety X, assume that the unramified relative local Langlands conjecture of Ben-Zvi-Sakellaridis-Venkatesh for X holds, the loop space LX is an L⁺G--placid ind--scheme, and there exists a dimension theory for LX, we give a spectral description of a full subcategory of Iwahori equivariant D-modules on LX in terms of the relative Langlands dual of X, confirming a slight variant of the tamely ramified local relative Langlands conjecture proposed by Devalapurkar.

Citations

• Proof of the geometric Langlands conjecture III: compatibility with parabolic induction
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• Quaternionic Satake equivalence
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• Singular support of coherent sheaves, and the geometric Langlands\n conjecture
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• On some finiteness questions for algebraic stacks
• Ind-coherent sheaves
• Equivariant Satake category and Kostant-Whittaker reduction
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Related

• Local Geometric Langlands Correspondence: the Spherical Case
• Local geometric Langlands correspondence and affine Kac-Moody algebras
• A `relative' local Langlands correspondence
• Langlands parameters for Moy-Prasad types
• Betti Geometric Langlands