Intertwining operator and h-harmonics associated with reflection groups

We study the intertwining operator and h-harmonics in Dunkl's theory on h-harmonics associated with reflection groups. Based on a biorthogonality between the ordinary harmonics and the action of the intertwining operator V on the harmonics, the main result provides a method to compute the action of the intertwining operator V on polynomials and to construct an orthonormal basis for the space of h-harmonics.