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On the construction of a finite Siegel space
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
dimensional space over a quadratic extension of a finite base field .
The orbits of the action of the symplectic group on Lagrangians are
described as homogeneous spaces. Also, Siegel's Space is described as the set
of anti-involutions of the symplectic group.2
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