Deformed diagonal harmonic polynomials for complex reflection groups

TL;DR

This paper introduces deformations of harmonic polynomial spaces for complex reflection groups and provides evidence that these deformed spaces are isomorphic to the original spaces as graded modules.

Contribution

It proposes a new deformation framework for harmonic polynomials associated with complex reflection groups and suggests their isomorphism to undeformed spaces.

Findings

Deformed harmonic polynomial spaces are likely isomorphic to original spaces.

Supports evidence for isomorphism as graded W-modules.

Extends understanding of harmonic polynomials in complex reflection groups.

Abstract

We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that this space seems to always be isomorphic, as a graded W-module, to the undeformed version.