Journal Article

Coxeter Groups and their Quotients Arising from Cluster Algebras

Anna Felikson and Pavel Tumarkin

in International Mathematics Research Notices

Volume 2016, issue 17, pages 5135-5186
Published in print January 2016 | ISSN: 1073-7928
Published online October 2015 | e-ISSN: 1687-0247 | DOI: https://dx.doi.org/10.1093/imrn/rnv282
Coxeter Groups and their Quotients Arising from Cluster Algebras

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In [1], Barot and Marsh presented an explicit construction of presentation of a finite Weyl group [math] 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 [math]. 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.

Journal Article.  14985 words.  Illustrated.

Subjects: Mathematics ; Pure Mathematics

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