The Geometric Weil Representation

TL;DR

This paper develops a geometric, invariant construction of the Weil representation over finite fields, highlighting underlying geometric phenomena and simplifying traditional formulas.

Contribution

It introduces a novel geometric and invariant approach to the Weil representation, avoiding specific realizations and complex formulas.

Findings

Provides a new geometric framework for Weil representation

Eliminates complex formulas present in traditional approaches

Highlights geometric phenomena underlying the representation

Abstract

In this paper we construct a geometric analogue of the Weil representation over a finite field. Our construction is principally invariant, not choosing any specific realization. This eliminates most of the unpleasant formulas that appear in the traditional (non-invariant) approaches, and puts in the forefront some delicate geometric phenomena which underlie this representation.