Demazure-Kashiwara cocycles and metaplectic geometry (Q1196137)

The Arnold-Maslov index, the metaplectic group and its natural actions on \(\Lambda_ 4\) (the 4 covering on the Lagrange-Grassmannian \(\Lambda)\) and its representation as a subgroup of \(Sp\times\mathbb{Z}/8\mathbb{Z}\) are derived by using only analytical properties of the metaplectic group and symplectic algebra without reference to algebraic topology. The approach provides a transparent representation of the main results.