Maslov indices on the metaplectic group \(Mp(n)\). (English) Zbl 0705.22013

de Gosson, Maurice

Ann. Inst. Fourier 40, No. 3, 537-555 (1990).

We use the properties of \(Mp(n)\) to construct functions \(\mu_{\ell}: Mp(n)\to {\mathbb{Z}}_ 8\) associated with the elements \(\ell\) of the lagrangian grassmannian \(\Lambda(n)\) which generalize the Maslov index on Mp(n) defined by J. Leray in his “Lagrangian Analysis” (1981; Zbl 0483.35002). We deduce from these constructions the identity between Mp(n) and a subset of \(Sp(n)\times {\mathbb{Z}}_ 8\), equipped with appropriate algebraic and topological structures.

Reviewer: M.de Gosson

MSC:

22E47	Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
37J99	Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D50	Geometric quantization

Keywords:

metaplectic group; Fourier transform; signature; index of inertia; Lagrangian; Grassmannian; Maslov index

Citations:

Zbl 0483.35002

References:

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