Reflection arrangements are hereditarily free (Q386795)

Let \(V\) be a finite-dimensional \(\mathbb{C}\)-vector space and \(W\subseteq\text{GL}(V)\) a finite unitary group generated by reflections at hyperplanes of \(V\). Let \({\mathcal A}\) denote the set of hyperplanes associated with the generating reflections and \(L\) the intersection lattice of \({\mathcal A}\). Terao proved that the reflection arrangement \({\mathcal A}\) is free. For a subspace \(X\in L\) one obtains the restricted arrangement of hyperplanes \({\mathcal A}^X\) by intersecting \(X\) with those hyperplanes \(\in{\mathcal A}\) not containing \(X\). When \(W\) is a Coxeter group and also when \(W\) is a Weyl group and in several exception cases it has been proved that \({\mathcal A}^X\) is also free.NEWLINENEWLINE The authors prove this result for the remaining exceptional cases using the CHVE package in GAP.