Generalization of Harish-Chandra's basic theorem for Riemannian symmetric spaces of non-compact type

A basic exact sequence by Harish-Chandra related to the invariant differential operators on a Riemannian symmetric space G/K is generalized for each K-type in a certain class which we call `single-petaled'. The argument also includes a further generalization of Broer's generalization of the Chevalley restriction theorem.