Symplectic geometry of semisimple orbits

2008/10/21 by Hassan Azad, Azad, Hassan, Erik P. van den Ban +4
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Symplectic Geometry (math.SG) #math.RT #math.SG

paper · pdf · doi:10.48550/arxiv.0810.3816

25 pages

arxiv created 2008/10/21 · openalex publication_date 2008/10/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any coadjoint orbit with real eigenvalues of a complex semisimple Lie group, equipped with the real part of the canonical holomorphic symplectic form, is symplectomorphic to the cotangent bundle of a (partial) flag manifold. Moreover, we generalize this result to hyperbolic orbits in a real semisimple Lie algebra.

Citations

• Symplectic manifolds and their lagrangian submanifolds

Related

• Canonical domains for coadjoint orbits
• Lagrangian submanifolds of Adjoint semisimple orbits given by real forms
• Orbits of real forms in complex flag manifolds
• The Orbits of the Symplectic Group on the Flag Manifold
• Symplectic and Hamiltonian properties of holomorphic coadjoint orbits