Hellmann, Chris; Langenbach, Brennan; VanValkenburgh, Michael Linear symplectomorphisms as \(R\)-Lagrangian subspaces. (English) Zbl 1380.37112 Involve 8, No. 4, 551-569 (2015). 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. Reviewer: Luc Vrancken (Valenciennes) 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 Keywords:complex symplectic linear algebra; linear symplectomorphism; Lagrangian submanifold; metaplectic representation PDFBibTeX XMLCite \textit{C. Hellmann} et al., Involve 8, No. 4, 551--569 (2015; Zbl 1380.37112) Full Text: DOI arXiv