Coxeter multiarrangements with quasi-constant multiplicities (Q1048217)

The paper under review generalizes results of \textit{H. Terao} [Invent. Math. 148, No.~3, 659--674 (2002; Zbl 1032.52013)] and \textit{M. Yoshinaga} [Proc. Japan Acad., Ser. A 78, No.~7, 116--119 (2002; Zbl 1034.32020)]. The main results concern structures of derivation modules for Coxeter arrangements with quasi-constant multiplicities; these are studied using the primitive derivation. The characteristic polynomial for a multiarrangement was defined in [\textit{T. Abe, H. Terao} and \textit{M. Wakefield}, Adv. Math. 215, No.~2, 825--838 (2007; Zbl 1123.52012)]. In general, the computation of this characteristic polynomial is difficult as it is not a combinatorial invariant. In the paper under review, the authors show that the characteristic polynomial of a Coxeter multiarrangement with quasi-constant multiplicity is combinatorially computable.