Reflection group relations arising from cluster algebras

Abstract

In this paper, we obtain relations in the Weyl groups of Kac-Moody algebras that come from mutation classes of skew-symmetrizable matrices. These relations generalize those obtained by Barot and Marsh for finite type. As an application, we obtain some combinatorial properties of the mutation classes of skew-symmetrizable matrices.

10 pages; minor changes

References in corpus (4)

• Coxeter groups and their quotients arising from cluster algebras
• Reflection group presentations arising from cluster algebras
• Companion bases for cluster-tilted algebras
• Cluster algebras and symmetric matrices

Cited by in corpus (2)

• Coxeter groups and their quotients arising from cluster algebras
• Coxeter groups, quiver mutations and geometric manifolds