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Quantization of symplectic vector spaces over finite fields.

Fri, 08/21/2009 - 19:51 — SomNambul
Authors: Shamgar Gurevich, Ronny Hadani
Subjects: Representation Theory
link: http://arxiv.org/abs/0705.4556
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.

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Mon, 01/09/2012 - 05:20 — yongling

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