Exceptional sequences and clusters

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.

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

References in corpus (1)

• Catalan numbers and Schubert polynomials for $w=1(n+1)...2$

Cited by in corpus (1)

• In which it is proven that, for each parabolic quasi-Coxeter element in a finite real reflection group, the orbits of the Hurwitz action on its reflection factorizations are distinguished by the two obvious invariants