Geodesic
Symplectic Killing spinors
Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 1, pp. 19-35.

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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.
Classification : 53C07, 58J60
Keywords: Fedosov manifolds; symplectic spinors; symplectic Killing spinors; symplectic Dirac operators; Segal-Shale-Weil representation 
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     title = {Symplectic {Killing} spinors},
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Krýsl, Svatopluk. Symplectic Killing spinors. Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 1, pp. 19-35. http://geodesic.mathdoc.fr/item/CMUC_2012__53_1_a1/