Year: 2007
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Gurevich, Shamgar, Hadani, Ronny
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1603314952