Poisson structures on complex flag manifolds associated with real forms

Details Poisson structures on complex flag manifolds associated with real forms Poisson structures on complex flag manifolds associated with real forms

2003-09-19

arxiv.org/abs/math/0309334v1

Mathematics

Symplectic Geometry

11 pages

Scientific paper

For a complex semi-simple group G and its real form G0 we define a Poisson structure on the flag variety of G such that all the Bruhat cells (for a suitable choice of a Borel subgroup of G) as well as all the G0-orbits are Poisson submanifolds. We show that each intersection of a G0-orbit with a Bruhat cell is a regular Poisson submanifold and we compute the dimensions of its symplectic leaves.

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