COXETER ARRANGEMENTS ARE HEREDITARILY FREE

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Abstract

A Coxeter arrangement is the set of reflecting hyperplanes in the reflection representation of a finite Coxeter group. Arnold and Saito showed that every Coxeter arrangement is free. We prove that any restriction of a Coxeter arrangement is again a free arrangement. It explains why the characteristic polynomial of any restriction of a Coxeter arrangement has only positive integer roots, which was observed by P. Orlik and L. Solomon. We use the classification of Coxeter groups.

Journal

  • Tohoku Mathematical Journal, Second Series

    Tohoku Mathematical Journal, Second Series 45(3), 369-383, 1993

    Tohoku University

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