Towards a categorical analogue of Gelfand-Kazhdan Theorem
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917795197878272 |
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| author | Popkovich, Alexander |
| author_facet | Popkovich, Alexander |
| contents | A celebrated theorem by Gelfand-Kazhdan states that the restriction of any cuspidal irreducible representations of $GL_n(\mathcal{K})$ over local field to the mirabolic subgroup $P$ is isomorphic to the standard irreducible representation of $P$. We formulate a conjecture that an analogous statement should hold for categorical representations. In this note we prove this for a particular example of an irreducible cuspidal categorical representation of $PGL_2(\mathcal{K})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards a categorical analogue of Gelfand-Kazhdan Theorem Popkovich, Alexander Representation Theory A celebrated theorem by Gelfand-Kazhdan states that the restriction of any cuspidal irreducible representations of $GL_n(\mathcal{K})$ over local field to the mirabolic subgroup $P$ is isomorphic to the standard irreducible representation of $P$. We formulate a conjecture that an analogous statement should hold for categorical representations. In this note we prove this for a particular example of an irreducible cuspidal categorical representation of $PGL_2(\mathcal{K})$. |
| title | Towards a categorical analogue of Gelfand-Kazhdan Theorem |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2410.02139 |