  Suppose that W is a finite, unitary reflection group acting on the complex
vector space V. Let A = A(W) be the associated hyperplane arrangement of W.
Terao has shown that each such reflection arrangement A is free. There is the
stronger notion of an inductively free arrangement. In 1992, Orlik and Terao
conjectured that each reflection arrangement is inductively free. It has been
known for quite some time that the braid arrangement as well as the Coxeter
arrangements of type B and type D are inductively free. Barakat and Cuntz
completed this list only recently by showing that every Coxeter arrangement is
inductively free.
  Nevertheless, Orlik and Terao's conjecture is false in general. In a recent
paper, we already gave two counterexamples to this conjecture among the
exceptional complex reflection groups.
  In this paper we classify all inductively free reflection arrangements. In
addition, we show that the notions of inductive freeness and that of hereditary
inductive freeness coincide for reflection arrangements.
  As a consequence of our classification, we get an easy, purely combinatorial
characterization of inductively free reflection arrangements A in terms of
exponents of the restrictions to any hyperplane of A.

Group Theory;Combinatorics