Reflection group presentations arising from cluster algebras
Group Theory
2020-12-21 v2 Combinatorics
Representation Theory
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.
Cite
@article{arxiv.1112.2300,
title = {Reflection group presentations arising from cluster algebras},
author = {Michael Barot and Bethany Marsh},
journal= {arXiv preprint arXiv:1112.2300},
year = {2020}
}
Comments
25 pages, no separate figure files. Definition of presentation simplified, taking account of symmetry, giving shorter proof of Thm. 5.2