Construction of Conformally Invariant Differential Operators
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We present a method of computation of the explicit form of conformally invariant differential operators on ℝn defined using the ambient metric construction. The action of the conformal group on the conformal compactification of ℝn is realised as the action of SO(n+1, 1) on the projectivisation of the null cone in the ambient space ℝ n+1, 1. We first review a class of differential operators on the ambient space, which give rise to the conformally invariant differential operators on ℝn, and then we present a method how to write down the explicit coefficients of the induced operator by means of a suitable adapted frame on the ambient space. The procedure gives an alternative and direct method how to compute the so-called higher symmetry operators for the Laplace equation introduced by M. Eastwood.
KeywordsSymmetry operators Laplace conformally invariant operators
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