metaplectic structure

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

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

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