A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups

摘要

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