Quantization of Symplectic Vector Spaces over Finite Fields
نویسندگان
چکیده
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 H(V ). 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.
منابع مشابه
Canonical Quantization of Symplectic Vector Spaces over Finite Fields
In this paper an affirmati5e answer is given to a question of D. Kazhdan on the existence of a canonical Hilbert spaces attached to symplectic vector spaces over finite fields. This result suggest a solution to a discrete analogue of a well known problem in geometric quantization where a naive canonical Hilbert space does not exist. As a result, a canonical model for the Weil representation of ...
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In these notes we construct a quantization functor, associating a Hilbert space H(V ) to a finite dimensional symplectic vector space V over a finite field Fq. 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 Stonevon Neumann theorem for the Heisenberg group over Fq. Our result an...
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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 Fq. 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 Fq. Our result ...
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