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

Abstract

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.

29 pages

References in corpus (2)

• Shintani lifts for Weil representations of unitary groups over finite fields
• An Exceptional Representation of Sp(4,F_q)

Cited by in corpus (2)

• Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations II: wild case
• Mod $\ell$ Weil representations and Deligne--Lusztig inductions for unitary groups