The Weil Representation in Characteristic Two

TL;DR

This paper introduces a novel variant of the Weil representation for symplectic vector spaces over characteristic two fields, expanding the symmetry group and formalism for clearer realization.

Contribution

It constructs a new Weil representation variant for characteristic two, involving a larger group and the development of canonical vector spaces for better understanding.

Findings

New Weil representation variant for characteristic two

Development of canonical vector spaces formalism

Realization of larger symmetry group

Abstract

In this paper we construct a new variant of the Weil representation, associated with a symplectic vector space V defined over a finite field of characteristic two. Our variant is a representation of a bigger group than that of Weil. In the course, we develop the formalism of canonical vector spaces, which enables us to realize the bigger symmetry group and the representation in a transparent manner.