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Keywords:
Fedosov manifolds; symplectic spinors; symplectic Killing spinors; symplectic Dirac operators; Segal-Shale-Weil representation
Fedosov manifolds; symplectic spinors; symplectic Killing spinors; symplectic Dirac operators; Segal-Shale-Weil representation
Summary:
Let $(M,\omega )$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla$. Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main object of this paper. We derive a necessary condition which has to be satisfied by a symplectic Killing spinor field. Using this condition one may easily compute the symplectic Killing spinor fields for the standard symplectic vector spaces and the round sphere $S^2$ equipped with the volume form of the round metric.
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