Notes on Canonical Quantization of Symplectic Vector Spaces over Finite Fields
Identifieur interne : 000398 ( Main/Exploration ); précédent : 000397; suivant : 000399Notes on Canonical Quantization of Symplectic Vector Spaces over Finite Fields
Auteurs : Shamgar Gurevich [États-Unis] ; Ronny Hadani [États-Unis]Source :
- Progress in Mathematics ; 2010.
Abstract
Summary: In these notes we construct a quantization functor, associating a Hilbert space $$\mathcal{H}(V )$$ to a finite dimensional symplectic vector space V over a finite field $${\mathbb{F}}_{q}$$ . As a result, we obtain a canonical model for the Weil representation of the symplectic group SpV . The main technical result is a proof of a stronger form of the Stone–von Neumann theorem for the Heisenberg group over $${\mathbb{F}}_{q}$$ . 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 $${\mathbb{F}}_{q}$$ .
Url:
DOI: 10.1007/978-0-8176-4831-2_8
Affiliations:
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