CARTAN-SIEGEL HOMOGENEOUS DOMAINS: SIEGEL DISK

Siegel Disk has been introduced by Carl Ludwig Siegel through Symplectic Group Sp_2nR that is one possible generalization of the group SL₂R = Sp₂R (group of invertible matrices with determinant 1) to higher dimensions. This generalization goes further; since they act on a symmetric homogeneous space, the Siegel upper half plane, and this action has quite a few similarities with the action of SL₂R on the Poincaré’s hyperbolic plane