Deformations of Coxeter hyperplane arrangements and their characteristic polynomials

Let A be a Coxeter hyperplane arrangement, that is the arrangement of reflecting hyperplanes of an irreducible finite Coxeter group. A deformation of A is an affine arrangement each of whose hyperplanes is parallel to some hyperplane of A. We survey some of the interesting combinatorics of classes of such arrangements, reflected in their characteristic polynomials. Much of the motivation for the study of arrangements of hyperplanes comes from Coxeter arrangements. Because of their importance in algebra, Coxeter arrangements have been studied a great deal in the context of representation theory of semisimple Lie algebras (where they arose)