Exceptional sequences and clusters

Details Exceptional sequences and clusters Exceptional sequences and clusters

2009-01-16

arxiv.org/abs/0901.2590v3

Mathematics

Representation Theory

19 pages, 2 figures. Appendix written with Hugh Thomas added in v2. Typos fixed and exposition improved in v3

Scientific paper

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.

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