We provide a type-independent construction of an explicit basis for the semi-invariant harmonic differential forms of an arbitrary pseudo-reflection group in characteristic zero. Equivalently, we completely describe the structure of the χ-isotypic components of the corresponding super coinvariant algebras in one commuting and one anti-commuting set of variables, for all linear characters χ. In type A, we verify a specialization of a conjecture of Zabrocki [37] which provides a representation-theoretic model for the Delta conjecture of Haglund–Remmel–Wilson [10]. Our “top-down” approach uses the methods of Cartan's exterior calculus and is in some sense dual to related work of Solomon [29], Orlik–Solomon [21], and Shepler [27], [28] describing (semi-)invariant differential forms.
