  Let $G$ be a complex reductive connected algebraic group equipped with the
Sklyanin bracket. A classification of Poisson homogeneous $G$-spaces with
connected isotropy subgroups is given. This result is based on Drinfeld's
correspondence between Poisson homogeneous $G$-spaces and Lagrangian
subalgebras in the double $D(g)$ (here $g = Lie G$). A geometric interpretation
of some of Poisson homogeneous $G$-spaces is also proposed.
