Geodesic
Ellipticity of the symplectic twistor complex
Archivum mathematicum, Tome 47 (2011) no. 4, pp. 309-327 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain infinite rank vector bundles defined over this manifold. The differential operators are symplectic analogues of the twistor operators known from Riemannian or Lorentzian spin geometry. It is known that the mentioned sequences form complexes if the symplectic connection is of Ricci type. In this paper, we prove that certain parts of these complexes are elliptic.
For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain infinite rank vector bundles defined over this manifold. The differential operators are symplectic analogues of the twistor operators known from Riemannian or Lorentzian spin geometry. It is known that the mentioned sequences form complexes if the symplectic connection is of Ricci type. In this paper, we prove that certain parts of these complexes are elliptic.
Classification : 22E46, 53C07, 53C80, 58J05
Keywords: Fedosov manifolds; Segal-Shale-Weil representation; Kostant’s spinors; elliptic complexes 
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Krýsl, Svatopluk. Ellipticity of the symplectic twistor complex. Archivum mathematicum, Tome 47 (2011) no. 4, pp. 309-327. http://geodesic.mathdoc.fr/item/ARM_2011_47_4_a6/

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