Exceptional sequences and clusters
Representation Theory
2012-09-13 v3 Group Theory
Abstract
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.
Cite
@article{arxiv.0901.2590,
title = {Exceptional sequences and clusters},
author = {Kiyoshi Igusa and Ralf Schiffler},
journal= {arXiv preprint arXiv:0901.2590},
year = {2012}
}
Comments
19 pages, 2 figures. Appendix written with Hugh Thomas added in v2. Typos fixed and exposition improved in v3