Exceptional sequences and clusters

By Kiyoshi Igusa, Ralf Schiffler. 2009

76 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/583db51f23b107ec89193ac7d2c31646a93b998e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Henning Krause
2. Andrew Hubery
3. Robert Sulway
4. David E. Speyer
5. Jon McCammond
6. Hugh Thomas
7. I. Reiten
8. B. Keller

In Geometry and Topology

1. Andrew Hubery
2. Hugh Thomas
3. Henning Krause
4. B. Keller
5. Robert Sulway
6. David E. Speyer
7. Jon McCammond
8. I. Reiten

In Statistical and Nonlinear Physics

1. Hugh Thomas
2. Andrew Hubery
3. Henning Krause
4. David E. Speyer
5. Xiao-Wu Chen
6. Apostolos Beligiannis
7. Peter Jørgensen
8. James Gillespie

Citations in the corpus

• Artin groups of Euclidean type (2013, background): “In 2010 Igusa and Schiffler proved transitivity of the Hurwitz action on reflection factorizations of Coxeter elements in Coxeter groups in complete generality [21] and in 2014 a short proof of this general fact was posted by Baumeister et al.”
• A categorification of non-crossing partitions (2013, background): “3 (Igusa–Schiffler [33], see also [2]).”
• Acyclic Cluster Algebras Revisited (2012, background): “Igusa and Schiffler [17] showed that, conversely, given any Coxeter factorization t1t2 · · · tn = c, there is an exceptional sequence (M1, .”