 
Summary: Advanced Studies in Pure Mathematics 2?, 199?
Singularities and Arrangements, SapporoTokyo 1998
pp. 126
Deformations of Coxeter hyperplane arrangements
and their characteristic polynomials
Christos A. Athanasiadis
Abstract.
Let A be a Coxeter hyperplane arrangement, that is the arrange
ment of reflecting hyperplanes of an irreducible finite Coxeter group.
A deformation of A is an affine arrangement each of whose hyper
planes is parallel to some hyperplane of A. We survey some of the
interesting combinatorics of classes of such arrangements, reflected
in their characteristic polynomials.
§1. Introduction
Much of the motivation for the study of arrangements of hyperplanes
comes from Coxeter arrangements. Because of their importance in alge
bra, Coxeter arrangements have been studied a great deal in the context
of representation theory of semisimple Lie algebras (where they arose),
invariant theory of reflection groups, combinatorics of root systems and
Coxeter groups, combinatorics of convex polytopes and oriented ma
