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Symplectic geometry

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

Abstract

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.

Keywords

Symplectic Form Symplectic Manifold Maximal Torus Symplectic Geometry Coadjoint Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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