nLab
metaplectic structure

Contents

Idea

For (X,ω)(X, \omega) a symplectic manifold a metaplectic structure on XX is a lift of structure groups of the tangent bundle from the symplectic group to the metaplectic group through the double cover map Mp(2n,)Sp(2n,)Mp(2n, \mathbb{R}) \to Sp(2n, \mathbb{R}):

BMp(2n,) metaplecticstructure X TX BSp(2n,). \array{ && \mathbf{B}Mp(2n, \mathbb{R}) \\ & {}^{\mathllap{metaplectic \atop structure}}\nearrow & \downarrow \\ X &\stackrel{T X}{\to}& \mathbf{B} Sp(2n, \mathbb{R}) } \,.

Revised on July 10, 2012 18:35:58 by David Corfield (129.12.18.29)