Symplectic geometry

  • Michèle Audin
Part of the Progress in Mathematics book series (PM, volume 93)


Before defining symplectic manifolds, recall a family of examples we shall use as a guide in this chapter. I am speaking of the \( {H_\lambda }'{\rm{s}} \) we have already met: \( {H_\lambda } \) is the set of all n x n hermitian matrices with given spectrum λ = (λ1,...,λn) ∈ Rn. We already know that \( {H_\lambda } \) is indeed a manifold, as an orbit of the compact group U(n) (see I–1.3) acting by conjugation on the vector space \( H \) of all hermitian matrices. Moreover the \( {H_\lambda }'{\rm{s}} \) are symplectic manifolds.


Symplectic Form Symplectic Manifold Maximal Torus Symplectic Geometry Coadjoint Orbit 
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Copyright information

© Birkhäuser Verlag Basel 1991

Authors and Affiliations

  • Michèle Audin
    • 1
  1. 1.IRMA Université Louis PasteurStrasbourg CedexFrance

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