θ-Series Associated to Quadratic forms
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.
KeywordsSymmetric Form Congruence Subgroup Maslov Index Dual Lattice Symplectic Space
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