Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866911778530656256 |
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| author | Imai, Naoki Tsushima, Takahiro |
| author_facet | Imai, Naoki Tsushima, Takahiro |
| contents | We give a geometric construction of the Heisenberg-Weil representation of a finite unitary group by the middle étale cohomology of an algebraic variety over a finite field, whose rational points give a unitary Heisenberg group. Using also a Frobenius action, we give a geometric realization of the Howe correspondence for $(\mathit{Sp}_{2n},O_2^-)$ over any finite field including characteristic two. As an application, we show that unipotency is preserved under the Howe correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_10226 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences Imai, Naoki Tsushima, Takahiro Representation Theory Number Theory 20C33, 11F27 We give a geometric construction of the Heisenberg-Weil representation of a finite unitary group by the middle étale cohomology of an algebraic variety over a finite field, whose rational points give a unitary Heisenberg group. Using also a Frobenius action, we give a geometric realization of the Howe correspondence for $(\mathit{Sp}_{2n},O_2^-)$ over any finite field including characteristic two. As an application, we show that unipotency is preserved under the Howe correspondence. |
| title | Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences |
| topic | Representation Theory Number Theory 20C33, 11F27 |
| url | https://arxiv.org/abs/1812.10226 |