Recursively free reflection arrangements

Let A=A(W) be the reflection arrangement of the finite complex reflection group W. By Terao's famous theorem, the arrangement A is free. In this paper we classify all reflection arrangements which belong to the smaller class of recursively free arrangements. Moreover for the case that W admits an irreducible factor isomorphic to G31 we obtain a new (computer-free) proof for the non-inductive freeness of A(W). Since our classification implies the non-recursive freeness of the reflection arrangement A(G31), we can prove a conjecture by Abe about the new class of divisionally free arrangements which he recently introduced.