Abstract
For a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure), we construct a sequence consisting of differential operators using a symplectic torsion-free affine connection. All but one of these operators are of first order. The first order ones are symplectic analogues of the twistor operators known from Riemannian spin geometry. We prove that under the condition the symplectic Weyl curvature tensor field of the symplectic connection vanishes, the mentioned sequence forms a complex. This gives rise to a new complex for the so called Ricci type symplectic manifolds, which admit a metaplectic structure.
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Communicated by A. Cap.
The author of this article was supported by the grant GAČR 201/08/0397 of the Grant Agency of Czech Republic. The work is a part of the research project MSM 0021620839 financed by MŠMT ČR.
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Krýsl, S. Complex of twistor operators in symplectic spin geometry. Monatsh Math 161, 381–398 (2010). https://doi.org/10.1007/s00605-009-0158-3
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DOI: https://doi.org/10.1007/s00605-009-0158-3
Keywords
- Fedosov manifolds
- Metaplectic structures
- Symplectic spinors
- Kostant spinors
- Segal-Shale-Weil representation
- Complexes of differential operators