2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140242In 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.A remark due to Ofer Gabber added (page 12). Accepted for publication (Selecta, December 2006)Representation TheoryAlgebraic GeometryQuantum Physicstext