Poisson structures on complex flag manifolds associated with real forms

Foth, Philip; Lu, Jiang-Hua

doi:10.1090/S0002-9947-05-03789-X

Poisson structures on complex flag manifolds associated with real forms
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by Philip Foth and Jiang-Hua Lu PDF

Trans. Amer. Math. Soc. 358 (2006), 1705-1714 Request permission

Abstract:

For a complex semisimple Lie group $G$ and a real form $G_0$ we define a Poisson structure on the variety of Borel subgroups of $G$ with the property that all $G_0$-orbits in $X$ as well as all Bruhat cells (for a suitable choice of a Borel subgroup of $G$) are Poisson submanifolds. In particular, we show that every non-empty intersection of a $G_0$-orbit and a Bruhat cell is a regular Poisson manifold, and we compute the dimension of its symplectic leaves.

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