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Poisson structures on complex flag manifolds associated with real forms

Philip Foth·Jiang-Hua Lu
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Abstract

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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Philip Foth, Jiang-Hua Lu. 2003-09-19. Poisson structures on complex flag manifolds associated with real forms. https://arxiv.org/abs/math/0309334

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