Exceptional sequences and clusters

Kiyoshi Igusa, Ralf Schiffler

Published 2009-01-16, updated 2009-12-21Version 3

We show that exceptional sequences for hereditary algebras are characterized by the fact that the product of the corresponding reflections is the inverse Coxeter element in the Weyl group. We use this result to give a new combinatorial characterization of clusters tilting sets in the cluster category in the case where the hereditary algebra is of finite type.