Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 026, 18 pages      arXiv:1612.01856      https://doi.org/10.3842/SIGMA.2017.026

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

Jean-Louis Clerc
Institut Elie Cartan de Lorraine, Université de Lorraine, France

Received December 07, 2016, in final form April 11, 2017; Published online April 19, 2017

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 $S^{n-1}$.

Key words: conformally covariant differential operators; Juhl's covariant differential operators.

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