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Symplectic spinor valued forms and invariant operators acting between them. (English) Zbl 1164.58320

Summary: Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described.

MSC:

58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
53C27 Spin and Spin\({}^c\) geometry
53D05 Symplectic manifolds (general theory)
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