Notes on quantization of symplectic vector spaces over finite fields
| dc.creator | Gurevich, Shamgar | |
| dc.creator | Hadani, Ronny | |
| dc.date | 2007-08-05 | |
| dc.date | 2009-04-20 | |
| dc.date.accessioned | 2026-07-07T13:05:24Z | |
| dc.date.available | 2026-07-07T13:05:24Z | |
| dc.description | 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. | |
| dc.description | Notes from the lecture at the AGAQ conference (Istanbul, June 2006) on our solution to Kazhdan's problem on canonical quantization | |
| dc.identifier | https://arxiv.org/abs/0708.0669 | |
| dc.identifier | http://arxiv.org/abs/0708.0669 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227477 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Representation Theory | |
| dc.title | Notes on quantization of symplectic vector spaces over finite fields | |
| dc.type | text |