Rigid Reflections of Rank 3 Coxeter Groups and Reduced Roots of Rank 2 Kac–Moody Algebras

被引：0
作者：
Kyu-Hwan Lee
Jeongwoo Yu
机构：
[1] University of Connecticut,Department of Mathematics
[2] Seoul National University,Department of Mathematical Sciences
来源：
Algebras and Representation Theory | 2023年 / 26卷
关键词：
Coxeter group; Kac–Moody algebra; Rigid reflection; Primary 20F55; 17B67; Secondary 16G20;
D O I：
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学科分类号：
摘要：
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.
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页码：1465 / 1496
页数：31
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