Quantization of symplectic vector spaces over finite fields
Representation Theory
2009-08-20 v4 Mathematical Physics
Algebraic Geometry
math.MP
Quantum Algebra
Symplectic Geometry
Quantum Physics
Abstract
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.
Cite
@article{arxiv.0705.4556,
title = {Quantization of symplectic vector spaces over finite fields},
author = {Shamgar Gurevich and Ronny Hadani},
journal= {arXiv preprint arXiv:0705.4556},
year = {2009}
}