Reflection group presentations arising from cluster algebras

Abstract

We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.

25 pages, no separate figure files. Definition of presentation simplified, taking account of symmetry, giving shorter proof of Thm. 5.2

References in corpus (1)

• Companion bases for cluster-tilted algebras

Cited by in corpus (4)

• Coxeter groups and their quotients arising from cluster algebras
• Coxeter groups, quiver mutations and geometric manifolds
• Reflection group relations arising from cluster algebras
• Cluster algebras and symmetric matrices