On a tamely ramified local relative Langlands conjecture via categorical representations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918177733083136 |
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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 |