A metaplectic structure [REF] on a symplectic manifold (M, \omega) is an equivariant lift of the symplectic frame bundle \pi_{\mathbf R}\colon{\mathbf R}\to M\, with respect to the double covering \rho\colon {\mathrm {Mp}}(n,{\mathbb R})\to {\mathrm {Sp}}(n,{\mathbb R}).\,
F_{\mathbf P_2}\circ f=F_{\mathbf P_1} and f({\mathbf p}q)=f({\mathbf p})q for all {\mathbf p}\in {\mathbf P_1} and q\in {\mathrm {Mp}}(n,{\mathbb R}).