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arXiv · 1812.10226

Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences

Naoki Imai·Takahiro Tsushima
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Abstract

We give a geometric construction of the Heisenberg-Weil representation of a finite unitary group by the middle \'{e}tale 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.

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BibTeXRIS

Naoki Imai, Takahiro Tsushima. 2018-12-26. Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences. https://doi.org/10.1007/s40879-023-00620-5

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