Canonical Quantization of Symplectic Vector Spaces over Finite Fields
نویسندگان
چکیده
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 the associated symplectic groups is obtained. Our construction use an idea suggested to us by J. Bernstein on the notion of enhanced Lagrangian subspace over a finite field.
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