Basic Definitions and Examples

  • Victor Guillemin
Part of the Progress in Mathematics book series (PM, volume 122)


Let G be a compact connected Lie group, g its Lie algebra, and g* the vector space dual of g. G acts on g by its adjoint action and on g* by the dual coadjoint action. The orbits of this action are compact simply-connected submanifolds of g*, and from now on we will refer to them simply as “coadjoint orbits.”


Symplectic Form Symplectic Manifold Coadjoint Orbit Hamiltonian Action Combinatorial Invariant 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Victor Guillemin
    • 1
  1. 1.Department of MathematicsMITCambridgeUSA

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