Relating Arthur packets of real unitary groups and $p$-adic symplectic and orthogonal groups
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910056115601408 |
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| author | Deng, Taiwang Huang, Chang Xu, Bin Zhao, Qixian |
| author_facet | Deng, Taiwang Huang, Chang Xu, Bin Zhao, Qixian |
| contents | We establish an explicit correspondence of certain Arthur packets between real unitary groups and $p$-adic symplectic or orthogonal groups. This allows one to compute Arthur packets of real unitary groups by translating results from the $p$-adic side. A main ingredient in our proof is an explicit relation between Zuckerman's translation functor on the real side and the Jacquet functor on the $p$-adic side. To achieve this, we construct a correspondence of stacks of Langlands parameters with fixed infinitesimal characters between the relevant real and $p$-adic groups. Our approach also allows one to relate the Kazhdan-Lusztig polynomials and the microlocal geometry between real and $p$-adic sides. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16314 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Relating Arthur packets of real unitary groups and $p$-adic symplectic and orthogonal groups Deng, Taiwang Huang, Chang Xu, Bin Zhao, Qixian Representation Theory Number Theory We establish an explicit correspondence of certain Arthur packets between real unitary groups and $p$-adic symplectic or orthogonal groups. This allows one to compute Arthur packets of real unitary groups by translating results from the $p$-adic side. A main ingredient in our proof is an explicit relation between Zuckerman's translation functor on the real side and the Jacquet functor on the $p$-adic side. To achieve this, we construct a correspondence of stacks of Langlands parameters with fixed infinitesimal characters between the relevant real and $p$-adic groups. Our approach also allows one to relate the Kazhdan-Lusztig polynomials and the microlocal geometry between real and $p$-adic sides. |
| title | Relating Arthur packets of real unitary groups and $p$-adic symplectic and orthogonal groups |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2603.16314 |