Reflection group presentations arising from cluster algebras
Presenter
October 30, 2012
Keywords:
- algebraic combinatorics
- commutative algebra
- cluster algebra
- reflection groups
- root systems
- Dynkin diagrams
- Coxeter groups
MSC:
- 13F60
- 13F55
- 13Fxx
- 13-xx
- 05-xx
- 06-xx
- 20F55
- 17B22
- 17Bxx
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 (without coefficients) and interpret the presentation in terms of companion bases in the associated root system.