Inductively free Multiderivations of Braid arrangements

TL;DR

This paper proves that the multiarrangements derived from Coxeter group type A reflection arrangements are inductively free, strengthening previous results on their freeness properties.

Contribution

It establishes that Coxeter type A reflection multiarrangements are inductively free, a stronger condition than previously known for these arrangements.

Findings

Coxeter type A reflection arrangements are inductively free.

Strengthens understanding of freeness properties of hyperplane arrangements.

Provides a new class of inductively free multiarrangements.

Abstract

The reflection arrangement of a Coxeter group is a well known instance of a free hyperplane arrangement. In 2002, Terao showed that equipped with a constant multiplicity each such reflection arrangement gives rise to a free multiarrangement. In this note we show that this multiarrangment satisfies the stronger property of inductive freeness in case the Coxeter group is of type $A$.