The Restricted Siegel Disc as Coadjoint Orbit

The restricted Siegel disc is a homogeneous space related to the connected component \(T_0(1)\) of the universal Teichmüller space via the period mapping. In this paper, we show that it is a coadjoint orbit of the universal central extension of the restricted symplectic group or, equivalently, an affine coadjoint orbit of the restricted symplectic group with cocycle given by the Schwinger term.