2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227477In these notes we construct a quantization functor, associating an Hilbert space H(V) to a finite dimensional symplectic vector space V over a finite field F_q. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp(V). The main technical result is a proof of a stronger form of the Stone-von Neumann theorem for the Heisenberg group over F_q. Our result answers, for the case of the Heisenberg group, a question of Kazhdan about the possible existence of a canonical Hilbert space attached to a coadjoint orbit of a general unipotent group over F_q.Notes from the lecture at the AGAQ conference (Istanbul, June 2006) on our solution to Kazhdan's problem on canonical quantizationMathematical PhysicsRepresentation Theorytext