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arXiv · 0705.4556

Quantization of symplectic vector spaces over finite fields

Shamgar Gurevich·Ronny Hadani
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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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Shamgar Gurevich, Ronny Hadani. 2009-08-20. Quantization of symplectic vector spaces over finite fields. https://arxiv.org/abs/0705.4556

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