  In 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.
