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.
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© 1980 Springer Science+Business Media New York
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Lion, G., Vergne, M. (1980). θ-Series Associated to Quadratic forms. In: The Weil representation, Maslov index and Theta series. Progress in Mathematics, vol 6. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4684-9154-8_17
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DOI: https://doi.org/10.1007/978-1-4684-9154-8_17
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Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3007-2
Online ISBN: 978-1-4684-9154-8
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