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Poisson structures on affine spaces and flag varieties. II. General case
K. R. Goodearl, M. Yakimov
The standard Poisson structures on the flag varieties G/P of a complex reductive algebraic group G are investigated. It is shown that the orbits of symplectic leaves in G/P under a…
Poisson structures on affine spaces and flag varieties. I. Matrix affine Poisson space
K. A. Brown, K. R. Goodearl, M. Yakimov
The standard Poisson structure on the rectangular matrix variety M_{m,n}(C) is investigated, via the orbits of symplectic leaves under the action of the maximal torus T of GL_{m+n}…
The Double and Dual of a Quasitriangular Lie Bialgebra
Timothy J. Hodges, Milen Yakimov
Let G be a connected, simply connected Poisson-Lie group with quasitriangular Lie bialgebra g. An explicit description of the double D(g) is given, together with the embeddings of…
Symplectic Leaves of Complex Reductive Poisson-Lie Groups
Milen Yakimov
All factorizable Lie bialgebra structures on complex reductive Lie algebras were described by Belavin and Drinfeld. We classify the symplectic leaves of the full class of correspon…
Deformation Quantization of Lagrangian Fiber Bundles
Nicolai Reshetikhin, Milen Yakimov
Let (M, \om) be a symplectic manifold. A Lagrangian fiber bundle π: M -> B determines a completely integrable system on M. First integrals of this system are the pull-backs of func…