Coxeter groups and their quotients arising from cluster algebras

Felikson, A.; Tumarkin, P.

Abstract

In [1], Barot and Marsh presented an explicit construction of presentation of a finite Weyl group W by any initial seed of corresponding cluster algebra, that is, by any diagram mutation-equivalent to an orientation of a Dynkin diagram with Weyl group W. We obtain similar 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.

Citation

Felikson, A., & Tumarkin, P. (2016). Coxeter groups and their quotients arising from cluster algebras. International Mathematics Research Notices, 2016(17), 5135-5186. https://doi.org/10.1093/imrn/rnv282

• Journal Article Type: Article
• Acceptance Date: Sep 4, 2015
• Online Publication Date: Oct 19, 2015
• Publication Date: Jan 1, 2016
• Deposit Date: Jul 10, 2013
• Publicly Available Date: Oct 19, 2016
• Journal: International Mathematics Research Notices
• Print ISSN: 1073-7928
• Electronic ISSN: 1687-0247
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 2016
• Issue: 17
• Pages: 5135-5186
• DOI: https://doi.org/10.1093/imrn/rnv282
• Public URL: https://durham-repository.worktribe.com/output/1480862
• Related Public URLs: http://arxiv.org/abs/1307.0672