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θ-Series Associated to Quadratic forms

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

Abstract

Let (E,S) be a k-dimensional vector space with a non-degenerate symmetric form of signature (p,q). We first consider the two-dimensional canonical symplectic space V = ℝP ⊕ℝQ and the associated symplectic space (E ⊗ V,S ⊗ B). The group O(S) × SL(2, ℝ) is naturally imbedded in Sp(S ⊗ B). The space ℓ = E ⊗ P is a Lagrangian subspace of E ⊗ V.

Keywords

Symmetric Form Congruence Subgroup Maslov Index Dual Lattice Symplectic Space 
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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