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

For a finite reflection subgroup G⩽O(n+1,1,R) of the conformal group of the sphere with standard conformal structure (Sn,[g0]), we geometrically derive differential-difference Dunkl version of the series of conformally invariant differential operators with symbols given by powers of Laplace operator. The construction can be regarded as a deformation of the Fefferman-Graham ambient metric construction of GJMS operators.