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Acyclic cluster algebras, reflection groups, and curves on a punctured disc

Felikson, A.; Tumarkin, P.

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Abstract

We establish a bijective correspondence between certain non-self-intersecting curves in an n-punctured disc and positive c-vectors of acyclic cluster algebras whose quivers have multiple arrows between every pair of vertices. As a corollary, we obtain a proof of Lee–Lee conjecture [15] on the combinatorial description of real Schur roots for acyclic quivers with multiple arrows, and give a combinatorial characterization of seeds in terms of curves in an n-punctured disc.

Citation

Felikson, A., & Tumarkin, P. (2018). Acyclic cluster algebras, reflection groups, and curves on a punctured disc. Advances in Mathematics, 340, 855-882. https://doi.org/10.1016/j.aim.2018.10.020

Journal Article Type Article
Acceptance Date Oct 15, 2018
Online Publication Date Oct 22, 2018
Publication Date Dec 15, 2018
Deposit Date Oct 23, 2017
Publicly Available Date Oct 16, 2018
Journal Advances in Mathematics
Print ISSN 0001-8708
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 340
Pages 855-882
DOI https://doi.org/10.1016/j.aim.2018.10.020
Related Public URLs https://arxiv.org/abs/1709.10360

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