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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
Posted:
September 22, 2005
MathSciNet review:
2186993
Full-text PDF Free Access
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Additional Information
Abstract: For a complex semisimple Lie group  and a real form  we define a Poisson structure on the variety of Borel subgroups of  with the property that all  -orbits in  as well as all Bruhat cells (for a suitable choice of a Borel subgroup of  ) are Poisson submanifolds. In particular, we show that every non-empty intersection of a  -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
Posted:
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 after
28 years from publication.
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