A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups
Eugene Karolinsky
Abstract
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.
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