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The universal covering group of the symplectic group

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

Abstract

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)
$$\tau ({{\ell }_{1}},{{\ell }_{2}},{{\ell }_{3}}) = \tau ({{\ell }_{1}},{{\ell }_{2}},{{\ell }_{4}}) + \tau ({{\ell }_{2}},{{\ell }_{3}},{{\ell }_{4}}) + \tau ({{\ell }_{3}},{{\ell }_{1}},{{\ell }_{4}}).$$

Keywords

Unitary Transformation Chain Condition Symplectic Group Maslov Index Fixed Element 
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

© 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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