Metaplectic structure

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Definition

A metaplectic structure on a symplectic manifold is a lifting of its gluing cocycle to the symplectic group Sp_2n(\R), to a gluing cocycle to the metaplectic group Mp_{2n}(\R). The metaplectic group is the double cover of the symplectic group.

Equivalently, it can be viewed as realizing a symplectic manifold as a principal Mp_{2n}(\R)-bundle that gives rise to its given realization as a Sp_{2n}(\R)-bundle.

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