In this paper, we construct a quantization functor, associating a
complex vector space $\cal{H}(V)$ to a finite-dimensional symplectic vector
space V over a finite field of odd characteristic. As a result, we obtain
a canonical model for the Weil representation of the symplectic group
Sp$(V )$. The main new technical result is a proof of a stronger form of
the Stone–von Neumann property for the Heisenberg group $H(V )$. Our
result answers, for the case of the Heisenberg group, a question of Kazhdan
about the possible existence of a canonical vector space attached
to a coadjoint orbit of a general unipotent group over finite field.