Deformations of Coxeter hyperplane arrangements and their characteristic polynomials

Abstract

Let $\mathcal{A}$ be a Coxeter hyperplane arrangement, that is the arrangement of reflecting hyperplanes of an irreducible finite Coxeter group. A deformation of $\mathcal{A}$ is an affine arrangement each of whose hyperplanes is parallel to some hyperplane of $\mathcal{A}$. We survey some of the interesting combinatorics of classes of such arrangements, reflected in their characteristic polynomials.