Another Approach to Juhl's Conformally Covariant Differential Operators from $S^n$ to $S^{n-1}$

Abstract

A family $({\mathbf{D}}_{\lambda }{)}_{\lambda \in \mathbb{C}}$ of differential operators on the sphere $S^n$ is constructed. The operators are conformally covariant for the action of the subgroup of conformal transformations of $S^n$ which preserve the smaller sphere $S^{n-1}\subset S^n$. The family of conformally covariant differential operators from $S^n$ to $S^{n-1}$ introduced by A. Juhl is obtained by composing these operators on $S^n$ and taking restrictions to $S^{n-1}$.

References in corpus (1)

• Symmetry breaking for representations of rank one orthogonal groups II

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