Introduction

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

Abstract

Relations between symplectic geometry, Maslov index, representations of the Heisenberg group and the Shale-Weil representation of the symplectic group are discussed in this chapter. We first give in 1.1 the basic definitions and properties of symplectic vector spaces, Lagrangian subspaces, the Heisenberg Lie algebra and the action of the symplectic group of those objects.

Keywords

Manifold Cove 

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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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