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Reflection group presentations arising from cluster algebras

2011/12/10 by Michael Barot, Barot, Michael, Bethany Marsh +1
Mathematics · #20F55 #51F15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Primary: 13F60 #Representation Theory (math.RT) #Secondary: 16G20

paper · doi:10.48550/arxiv.1112.2300

openalex publication_date 2011/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.

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