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arXiv · 2510.25231

On a tamely ramified local relative Langlands conjecture via categorical representations

Milton Lin·Toan Pham·Jize Yu
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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.

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Milton Lin, Toan Pham, Jize Yu. 2025-10-29. On a tamely ramified local relative Langlands conjecture via categorical representations. https://arxiv.org/abs/2510.25231

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