Displaying similar documents to “Symplectic spinor valued forms and invariant operators acting between them”

Ellipticity of the symplectic twistor complex

Svatopluk Krýsl (2011)

Archivum Mathematicum

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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...

Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds

Svatopluk Krýsl (2007)

Archivum Mathematicum

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Consider a flat symplectic manifold ( M 2 l , ω ) , l ≥ 2 , admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If λ is an eigenvalue of the symplectic Dirac operator such that - ı l λ is not a symplectic Killing number, then l - 1 l λ is an eigenvalue of the symplectic Rarita-Schwinger operator.

Symplectic twistor operator and its solution space on ℝ 2

Marie Dostálová, Petr Somberg (2013)

Archivum Mathematicum

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We introduce the symplectic twistor operator T s in symplectic spin geometry of real dimension two, as a symplectic analogue of the Dolbeault operator in complex spin geometry of complex dimension 1. Based on the techniques of the metaplectic Howe duality and algebraic Weyl algebra, we compute the space of its solutions on ℝ 2 .