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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Poisson structures on complex flag manifolds associated with real forms


Authors: Philip Foth and Jiang-Hua Lu
Journal: Trans. Amer. Math. Soc. 358 (2006), 1705-1714
MSC (2000): Primary 53D17; Secondary 14M15, 22E15
Published electronically: September 22, 2005
MathSciNet review: 2186993
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Philip Foth
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721-0089
Email: foth@math.arizona.edu

Jiang-Hua Lu
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong
Email: jhlu@maths.hku.hk

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03789-X
PII: S 0002-9947(05)03789-X
Keywords: Lie groups, real forms, flag varieties, Poisson structures, symplectic leaves
Received by editor(s): September 30, 2003
Received by editor(s) in revised form: June 16, 2004
Published electronically: September 22, 2005
Dedicated: Dedicated to Alan Weinstein on the occasion of his 60th birthday
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.