%0 Generic %1 imai2018geometric %A Imai, Naoki %A Tsushima, Takahiro %D 2018 %K Oscillator howe weil %R 10.1007/s40879-023-00620-5 %T Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences %U http://arxiv.org/abs/1812.10226 %X 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 $(Sp_2n,O_2^-)$ over any finite field including characteristic two. As an application, we show that unipotency is preserved under the Howe correspondence.

@misc{imai2018geometric, 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.}, added-at = {2023-05-01T13:38:39.000+0200}, author = {Imai, Naoki and Tsushima, Takahiro}, biburl = {https://www.bibsonomy.org/bibtex/2af45630d269235516f33b1bda3aed3da/dragosf}, description = {Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences}, doi = {10.1007/s40879-023-00620-5}, interhash = {f6df2eb05a53bb948913aa25a6674b61}, intrahash = {af45630d269235516f33b1bda3aed3da}, keywords = {Oscillator howe weil}, note = {cite arxiv:1812.10226Comment: 29 pages}, timestamp = {2023-05-01T13:38:39.000+0200}, title = {Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences}, url = {http://arxiv.org/abs/1812.10226}, year = 2018 }