SPECHT POLYNOMIALS AND MODULES OVER THE WEYL ALGEBRA II

In this paper, we study an irreducible decomposition structure of the $$\mathcal {D}$$ -module direct image $$\pi _+(\mathcal {O}_{\mathbb {c}^n})$$ for finite map : \mathbb {C}^n \rightarrow {C}^n/ ({\mathcal {S}_{n_1}\times \cdots \times \mathcal {S}_{n_r}}).$$ We explicitly construct simple components {C}^n})$$ by providing their generators and multiplicities. Using equivalence categories higher Specht polynomials, describe a polynomial ring localized at discriminant $$\pi$$ . Furthermore, action invariant differential operators on polynomials.