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Linear symplectomorphisms as \(R\)-Lagrangian subspaces. (English) Zbl 1380.37112

From the introduction: The graph of a real linear symplectomorphism is an \(\mathbb R\)-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely imaginary and may be expressed in terms of the generating function of the transformation. The author provides explicit formulas; and moreover, as an application, he gives an explicit general formula for the metaplectic representation of the real symplectic group.

MSC:

37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010)
53D12 Lagrangian submanifolds; Maslov index
70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
81S10 Geometry and quantization, symplectic methods
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