Azada, Hassan ; van den Ban, Erik ; Biswas, Indranil (2008) Symplectic geometry of semisimple orbits Indagationes Mathematicae, 19 (4). pp. 507533. ISSN 00193577

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00193...
Related URL: http://dx.doi.org/10.1016/S00193577(09)00010X
Abstract
Let G be a complex semisimple group, T ⊂ G a maximal torus and B a Borel subgroup of G containing T. Let Ω be the KostantKirillov holomorphic symplectic structure on the adjoint orbit O = Ad(G)c ≈ G/Z(c), where c ∈ Lie(T), and Z(c) is the centralizer of c in G. We prove that the real symplectic form Re Ω (respectively, Im Ω) on O is exact if and only if all the eigenvalues ad(c) are real (respectively, purely imaginary). Furthermore, each of these real symplectic manifolds is symplectomorphic to the cotangent bundle of the partial flag manifold G/Z(cc)B, equipped with the Liouville symplectic form. The latter result is generalized to hyperbolic adjoint orbits in a real semisimple Lie algebra.
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Deposited On:  18 Oct 2010 10:11 
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