Another Approach to Juhl's Conformally Covariant Differential Operators from Sⁿ to Sⁿ⁻¹

Abstract

A family (Dλ)λ∈C of differential operators on the sphere Sⁿ is constructed. The operators are conformally covariant for the action of the subgroup of conformal transformations of Sⁿ which preserve the smaller sphere Sⁿ⁻¹ ⊂Sⁿ. The family of conformally covariant differential operators from Sⁿ to Sⁿ⁻¹ introduced by A. Juhl is obtained by composing these operators on Sⁿ and taking restrictions to Sⁿ⁻¹ .