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Deformations of Coxeter hyperplane arrangements and their characteristic polynomials. (English) Zbl 0976.32016
Falk, Michael (ed.) et al., Arrangements - Tokyo 1998. Proceedings of a workshop on mathematics related to arrangements of hyperplanes, Tokyo, Japan, July 13-18, 1998. In honor of the 60th birthyear of Peter Orlik. Tokyo: Kinokuniya Company Ltd. Adv. Stud. Pure Math. 27, 1-26 (2000).
Let $${\mathcal A}$$ be a Coxeter hyperplane arrangement, i.e. an arrangement of reflecting hyperplanes of an irreducible finite Coxeter group. A deformations of $${\mathcal A}$$ is an affine arrangement such that the hyperplanes are parallel to some hyperplane of $${\mathcal A}$$.
A survey about the work on deformation of Coxeter arrangements concerning the combinatorial and algebraic properties related to their characteristic polynomial is given.
For the entire collection see [Zbl 0952.00034].

##### MSC:
 32S22 Relations with arrangements of hyperplanes 52C30 Planar arrangements of lines and pseudolines (aspects of discrete geometry)
##### Keywords:
Coxeter hyperplane arrangement; deformation; survey