Displaying similar documents to “Symplectic Killing spinors”

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 spinor valued forms and invariant operators acting between them

Svatopluk Krýsl (2006)

Archivum Mathematicum

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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.