Notes on quantization of symplectic vector spaces over finite fields
Mathematical Physics
2009-04-20 v3 math.MP
Representation Theory
Abstract
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.
Cite
@article{arxiv.0708.0669,
title = {Notes on quantization of symplectic vector spaces over finite fields},
author = {Shamgar Gurevich and Ronny Hadani},
journal= {arXiv preprint arXiv:0708.0669},
year = {2009}
}
Comments
Notes from the lecture at the AGAQ conference (Istanbul, June 2006) on our solution to Kazhdan's problem on canonical quantization