%0 Journal Article
%T Quantization of symplectic vector spaces over finite fields
%A Shamgar Gurevich
%A Ronny Hadani
%J Mathematics
%D 2007
%I arXiv
%X In this paper, we construct a quantization functor, associating a complex vector space 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. 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.
%U http://arxiv.org/abs/0705.4556v4