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arXiv · 1405.6252

On the construction of a finite Siegel space

Jorge Soto Andrade·Jose Pantoja·Jorge A. Vargas
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Abstract

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 $2n$ dimensional space over a quadratic extension $E$ of a finite base field $F$. The orbits of the action of the symplectic group $Sp(n,F)$ on Lagrangians are described as homogeneous spaces. Also, Siegel's Space is described as the set of anti-involutions of the symplectic group.22

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Jorge Soto Andrade, Jose Pantoja, Jorge A. Vargas. 2014-05-24. On the construction of a finite Siegel space. https://arxiv.org/abs/1405.6252

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