Coxeter and crystallographic arrangements are inductively free

TL;DR

This paper proves that all crystallographic arrangements, including Coxeter arrangements like type E8, are hereditarily inductively free, expanding understanding of their algebraic and combinatorial properties.

Contribution

It establishes that crystallographic arrangements are hereditarily inductively free, a significant extension of the theory of free arrangements, including all Coxeter arrangements.

Findings

Crystallographic arrangements are hereditarily inductively free.

All Coxeter arrangements are inductively free.

Includes the arrangement of type E8.

Abstract

Using the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily inductively free. In particular, all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of type $E_8$. With little extra work we prove that also all Coxeter arrangements are inductively free.