On the lattice model of the Weil representation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914970984251392 |
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| author | Wang, Chun-Hui |
| author_facet | Wang, Chun-Hui |
| contents | Let F be a local field. In the case of F being the real field, Pierre Cartier constructed Heisenberg-Weil representations of a Heisenberg group in families using non-self-dual lattices. This result was later reformulated by Jae-Hyun Yang in another paper. We extend this family of representations to a representation of a Jacobi subgroup by incorporating a rational Metaplectic group. In the case of F being a non-archimedean local field of odd residual characteristic or a finite unramified extension of the field of 2-adic numbers, we obtain similar results for a Jacobi group by incorporating a Metaplectic group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03983 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the lattice model of the Weil representation Wang, Chun-Hui Representation Theory Number Theory Let F be a local field. In the case of F being the real field, Pierre Cartier constructed Heisenberg-Weil representations of a Heisenberg group in families using non-self-dual lattices. This result was later reformulated by Jae-Hyun Yang in another paper. We extend this family of representations to a representation of a Jacobi subgroup by incorporating a rational Metaplectic group. In the case of F being a non-archimedean local field of odd residual characteristic or a finite unramified extension of the field of 2-adic numbers, we obtain similar results for a Jacobi group by incorporating a Metaplectic group. |
| title | On the lattice model of the Weil representation |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2404.03983 |