Structure of the kernel of higher spin Dirac operators

Martin Plechšmíd

Displaying similar documents to “Structure of the kernel of higher spin Dirac operators”

BGG sequences on spheres

Petr Somberg (2000)

Commentationes Mathematicae Universitatis Carolinae

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BGG sequences on flat homogeneous spaces are analyzed from the point of view of decomposition of appropriate representation spaces on irreducible parts with respect to a maximal compact subgroup, the so called $K$ -types. In particular, the kernels and images of all standard invariant differential operators (including the higher spin analogs of the basic twistor operator), i.e. operators appearing in BGG sequences, are described.

Higher monogenicity and residue theorem for Rarita-Schwinger operator

Somberg, Petr

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Twistor operators on conformally flat spaces

Somberg, Petr

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Summary: We describe explicitly the kernels of higher spin twistor operators on standard even dimensional Euclidean space $ℛ^{2 l}$ , standard even dimensional sphere $S^{2 l}$ , and standard even dimensional hyperbolic space $ℋ^{2 l}$ , using realizations of invariant differential operators inside spinor valued differential forms. The kernels are finite dimensional vector spaces (of the same cardinality) generated by spinor valued polynomials on $ℛ^{2 l}, S^{2 l}, ℋ^{2 l}$ .