Geometric Weil representation in characteristic two

TL;DR

This paper constructs a geometric analog of the Weil representation for a metaplectic extension of symplectic groups over a ring of Witt vectors in characteristic two, using group stacks and triangulated categories.

Contribution

It introduces a novel geometric framework for the Weil representation in characteristic two via group stacks and triangulated categories, extending classical representation theory.

Findings

Construction of the group stack hat G over k.

Development of a geometric analog of the Weil representation.

Establishment of an action of hat G on a triangulated category.

Abstract

Let k be an algebraically closed field of characteristic two. Let R be the ring of Witt vectors of length two over k. We construct a group stack \hat G over k, the metaplectic extension of the Greenberg realization of Sp_{2n}(R). We also construct a geometric analog of the Weil representation of \hat G, this is a triangulated category on which \hat G acts by functors. This triangulated category and the action are geometric in a suitable sense.