Harmonic polynomials associated with reflection groups

We extend Maxwell's representation of harmonic polynomials to h-harmonics associated to a reflection invariant weight function h(k). Let D-i, 1 less than or equal to i less than or equal to d, be Dunkl's operators associated with a reflection group. For any homogeneous polynomial P of degree n, we prove the polynomial \x\P2 gamma +d-2+2n(D){1/\x\(2 gamma +d-2)} is a h-harmonic polynomial of degree n, where gamma = Sigma (ki) and D = (D-1, ..., D-d). The construction yields a basis for h-harmonics. We also discuss self-adjoint operators acting on the space of h-harmonics.