  The restricted Siegel disc is a homogeneous space related to the connected
component $T_0(1)$ of the Universal Teichm\"uller 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.
