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Coxeter groups and their quotients arising from cluster algebras.

Felikson, A. and Tumarkin, P. (2016) 'Coxeter groups and their quotients arising from cluster algebras.', International mathematics research notices., 2016 (17). pp. 5135-5186.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1093/imrn/rnv282
Publisher statement:This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Felikson, A. & Tumarkin, P. (2016). Coxeter groups and their quotients arising from cluster algebras. International Mathematics Research Notices, 2016(17): 5135-5186 is available online at: http://dx.doi.org/10.1093/imrn/rnv282
Record Created:07 Sep 2015 10:20
Last Modified:23 Oct 2016 00:38

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