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Coxeter groups and their quotients arising from cluster algebras

Felikson, A.; Tumarkin, P.

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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
Related Public URLs http://arxiv.org/abs/1307.0672

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Copyright 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




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