In this paper we study the decomposition of the direct image of Ï+(OX) the polynomial ring OX as a D-module, under the map Ï: spec OX âspec OXG(r,n), where OXG(r,n) is the ring of invariant polynomial under the action of the wreath product G(r, p):= Z/rZ ~Sn. We first describe the generators of the simple components of Ï+(OX) and give their multiplicities. Using an equivalence of categories and the higher Specht polynomials, we describe a D-module decomposition of the polynomial ring localized at the discriminant of Ï. Furthermore, we study the action invariants, differential operators, on the higher Specht polynomials