Coxeter groups and their quotients arising from cluster algebras
Abstract
In a recent paper, Barot and Marsh presented an explicit construction of presentation of a finite Weyl group by any seed of corresponding cluster algebra, i.e. by any diagram mutation-equivalent to an orientation of a Dynkin diagram with given Weyl group. Extending their construction to the affine case, we obtain presentations for all affine Coxeter groups. Furthermore, we generalize the construction to the settings of diagrams arising from unpunctured triangulated surfaces and orbifolds, which leads to presentations of corresponding groups as quotients of numerous distinct Coxeter groups.
Cite
@article{arxiv.1307.0672,
title = {Coxeter groups and their quotients arising from cluster algebras},
author = {Anna Felikson and Pavel Tumarkin},
journal= {arXiv preprint arXiv:1307.0672},
year = {2019}
}
Comments
34 pages, lots of figures; v4: relations for groups arising from surfaces/orbifolds cluster algebras and from exceptional mutation-finite cluster algebras are updated; some defining relations for affine groups are removed due to observed redundancy