θ-Series Associated to Quadratic forms

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


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.


Symmetric Form Congruence Subgroup Maslov Index Dual Lattice Symplectic Space 
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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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