The universal covering group of the symplectic group

  • Gérard Lion
  • Michèle Vergne
Part of the Progress in Mathematics book series (PM, volume 6)


Let ∧ be the manifold of all Lagrangian planes. The group G = Sp(B) acts on ∧. We have constructed in 1.5 a ℤ-valued function τ(ℓ1,ℓ2,ℓ2) on triples of Lagrangian planes. This function τ is invariant under the action of G and satisfies the chain condition (1.5.8)
$$\tau ({{\ell }_{1}},{{\ell }_{2}},{{\ell }_{3}}) = \tau ({{\ell }_{1}},{{\ell }_{2}},{{\ell }_{4}}) + \tau ({{\ell }_{2}},{{\ell }_{3}},{{\ell }_{4}}) + \tau ({{\ell }_{3}},{{\ell }_{1}},{{\ell }_{4}}).$$


Unitary Transformation Chain Condition Symplectic Group Maslov Index Fixed Element 
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Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Gérard Lion
    • 1
  • Michèle Vergne
    • 2
  1. 1.X U.E.R. de Sciences EconomiquesUniversité de ParisNanterreFrance
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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