2021/03/04 by Kyu‐Hwan Lee, Lee, Kyu-Hwan, Jeongwoo Yu +1
Mathematics · #16G20 #17B67 #20F55 #51F15 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2103.02836
openalex publication_date 2021/03/04 · openalex created_date 2022/07/16 · openalex updated_date 2026/07/28
In a recent paper by K.-H. Lee and K. Lee, rigid reflections are defined for any Coxeter group via non-self-intersecting curves on a Riemann surface with labeled curves. When the Coxeter group arises from an acyclic quiver, the rigid reflections are related to the rigid representations of the quiver. For a family of rank 3 Coxeter groups, it was conjectured in the same paper that there is a natural bijection from the set of reduced positive roots of a symmetric rank 2 Kac--Moody algebra onto the set of rigid reflections of the corresponding rank 3 Coxeter group. In this paper, we prove the conjecture.