On the Invariants of the Cohomology of Complements of Coxeter Arrangements

TL;DR

This paper refines the understanding of the cohomology invariants of Coxeter arrangement complements, confirming a conjecture by Felder and Veselov with explicit basis construction.

Contribution

It completes the verification of Felder and Veselov's conjecture by explicitly describing the basis of W-invariants in the cohomology ring.

Findings

Confirmed the explicit basis of W-invariants

Refined Brieskorn's cohomology analysis

Validated the conjecture by Felder and Veselov

Abstract

We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group $W$. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the space of $W$-invariants in this cohomology ring.