Spectrum generating on twistor bundle

Thomas Branson; Doojin Hong

Displaying similar documents to “Spectrum generating on twistor bundle”

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 $ℛ^{2 l}, S^{2 l}, ℋ^{2 l}$ .

On conformal powers of the Dirac operator on spin manifolds

Matthias Fischmann (2014)

Archivum Mathematicum

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The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm we recover explicit formula for the conformal third and present a conformal fifth power of the...

Transitive conformal holonomy groups

Jesse Alt (2012)

Open Mathematics

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For (M, [g]) a conformal manifold of signature (p, q) and dimension at least three, the conformal holonomy group Hol(M, [g]) ⊂ O(p + 1, q + 1) is an invariant induced by the canonical Cartan geometry of (M, [g]). We give a description of all possible connected conformal holonomy groups which act transitively on the Möbius sphere S p,q, the homogeneous model space for conformal structures of signature (p, q). The main part of this description is a list of all such groups which also act...