On a tamely ramified local relative Langlands conjecture via categorical representations

Fuente: arXiv
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Main Authors: Lin, Milton, Pham, Toan, Yu, Jize
Format: Preprint
Published: 2025
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author Lin, Milton
Pham, Toan
Yu, Jize
author_facet Lin, Milton
Pham, Toan
Yu, Jize
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_25231
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On a tamely ramified local relative Langlands conjecture via categorical representations
Lin, Milton
Pham, Toan
Yu, Jize
Representation Theory
Number Theory
22E57
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.
title On a tamely ramified local relative Langlands conjecture via categorical representations
topic Representation Theory
Number Theory
22E57
url https://arxiv.org/abs/2510.25231