Maslov indices on the metaplectic group \(Mp(n)\) (Q917724)

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 \textit{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.