Summary: Advanced Studies in Pure Mathematics 2?, 199?
Singularities and Arrangements, Sapporo-Tokyo 1998
Deformations of Coxeter hyperplane arrangements
and their characteristic polynomials
Christos A. Athanasiadis
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.
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-