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    On the construction of a finite Siegel space

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    In this note we construct a finite analogue of classical Siegel's Space. Our approach is to look at it as a non commutative Poincare's half plane. The finite Siegel Space is described as the space of Lagrangians of a 2n2n dimensional space over a quadratic extension EE of a finite base field FF. The orbits of the action of the symplectic group Sp(n,F)Sp(n,F) on Lagrangians are described as homogeneous spaces. Also, Siegel's Space is described as the set of anti-involutions of the symplectic group.2

    EEOC v. Razzoo\u27s, Inc.

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