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Conformally invariant differential operators on Minkowski space and their curved analogues. (English) Zbl 0659.53047
This article describes the construction of a natural family of conformally invariant differential operators on a four-dimensional (pseudo-) Riemannian manifold. Included in this family are the usual massless field equations for arbitrary helicity but there are many more besides. The article begins by classifying the invariant operators on flat space. This is a fairly straightforward task in representation theory best solved through the theory of Verma modules. The method generates conformally invariant operators in the curved case by means of Penrose’s local twistor transport.

MSC:
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
58J70 Invariance and symmetry properties for PDEs on manifolds
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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