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

Felikson, A.; Tumarkin, P.

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
• Public URL: https://durham-repository.worktribe.com/output/1373223
• Related Public URLs: https://arxiv.org/abs/1709.10360