  We give a type-independent construction of an explicit basis for the
semi-invariant harmonic differential forms of an arbitrary pseudo-reflection
group in characteristic zero. Our "top-down" approach uses the methods of
Cartan's exterior calculus and is in some sense dual to related work of
Solomon, Orlik--Solomon, and Shepler describing (semi-)invariant differential
forms. We apply our results to a recent conjecture of Zabrocki which provides a
representation theoretic-model for the Delta conjecture of
Haglund--Remmel--Wilson in terms of a certain non-commutative coinvariant
algebra for the symmetric group. In particular, we verify the alternating
component of a specialization of Zabrocki's conjecture.
