On the construction of a finite Siegel space
Representation Theory
2014-05-27 v1
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 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.22
Keywords
Cite
@article{arxiv.1405.6252,
title = {On the construction of a finite Siegel space},
author = {Jorge Soto Andrade and Jose Pantoja and Jorge A. Vargas},
journal= {arXiv preprint arXiv:1405.6252},
year = {2014}
}