English

Poisson structures on complex flag manifolds associated with real forms

Symplectic Geometry 2007-05-23 v1 Representation Theory

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.

Keywords

Cite

@article{arxiv.math/0309334,
  title  = {Poisson structures on complex flag manifolds associated with real forms},
  author = {Philip Foth and Jiang-Hua Lu},
  journal= {arXiv preprint arXiv:math/0309334},
  year   = {2007}
}

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11 pages