# nLab metaplectic structure

### Context

#### Symplectic geometry

symplectic geometry

higher symplectic geometry

# Contents

## Idea

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)