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For a finite reflection subgroup $G\leq O(n+1,1,\mR)$ of the conformal groupof the sphere with standard conformal structure $(S^n,[g_0])$, we geometricallyderive differential-difference Dunkl version of the series of conformallyinvariant differential operators with symbols given by powers of Laplaceoperator. The construction can be regarded as a deformation of theFefferman-Graham ambient metric construction of GJMS operators.

Finite reflection groups and the Dunkl-Laplace differential-difference operators in conformal geometry