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

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

Zbl 0483.35002
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### References:

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