论文标题
伪反射组的谐波差异形式I.半不变
Harmonic differential forms for pseudo-reflection groups I. Semi-invariants
论文作者
论文摘要
我们为特征零的任意伪反射组的半不变谐波差异形式的明确基础提供了独立的构造。我们的“自上而下”方法采用了Cartan的外部微积分的方法，在某种意义上是对所罗门，Orlik-Solomon和Shepler的相关工作的双重偶尔，描述了（半）不变的微分形式。我们将结果应用于最近的Zabrocki的猜想，该猜想为Haglund--Remmel的三角洲猜想提供了代表理论模型，就某些非共同的共同代数的代数而言。特别是，我们验证了Zabrocki猜想的专业化的交替组成部分。
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.
