Power sum decompositions of defining equations of reflection arrangements

TL;DR

This paper calculates the Waring rank of the fundamental skew invariant for complex reflection groups with regular highest degrees, covering all irreducible real reflection groups.

Contribution

It provides the first explicit determination of the Waring rank for these invariants across a broad class of reflection groups.

Findings

Waring rank determined for all complex reflection groups with regular highest degree

Includes all irreducible real reflection groups

Advances understanding of polynomial decompositions in reflection arrangements

Abstract

We determine the Waring rank of the fundamental skew invariant of any complex reflection group whose highest degree is a regular number. This includes all irreducible real reflection groups.