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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:182

Article

关键词: Coinvariant algebras;    Pseudo-reflection groups;    Harmonics;    Semi-invariants;    Invariant theory;   

DOI  :  10.1016/j.jcta.2021.105474

来源: Elsevier

【 摘 要 】

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 chi-isotypic components of the corresponding super coinvariant algebras in one commuting and one anti-commuting set of variables, for all linear characters chi. 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. (C) 2021 The Author(s). Published by Elsevier Inc.

【 授权许可】

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