Higher Specht Polynomials and Modules Over the Weyl Algebra (original) (raw)

In this paper, we study an irreducible decomposition structure of the D-module direct image π + (O C n) for the finite map π : C n → C n /(S n1 × • • • × S nr). We explicitly construct the simple component of π + (O C n) by providing their generators and their multiplicities. Using an equivalence categories and the higher Specht polynomials, we describe a D-module decomposition of the of the polynomial ring localized at the discriminant of π. Furthermore we study the action invariants differential operators on the higher Specht polynomials.