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.

我们为特征零中任意伪反射组的半不变谐波差分形式提供了显式基础的类型无关构造。同样地，我们完整地描述的结构χ在一个通勤和一个变量抗通勤组对应的超级coinvariant代数-isotypic组分，所有线性字符χ。在A型，我们验证了Zabrocki猜想的专业化[37]，它为Haglund–Remmel–Wilson的Delta猜想提供了表示理论模型[10]。我们的“自上而下”方法使用了Cartan的外部演算方法，并且在某种意义上与所罗门[29]，奥尔里克–所罗门[21]和谢普勒[27]，[28]的相关工作双重描述（半）不变的微分形式。