Harmonic differential forms for pseudo-reflection groups I. Semi-invariants

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