Rigid reflections and Kac-Moody algebras

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（7）
• 页码范围: 1317-1330
• 页数: 14页
• 语种: 英文

摘要

Given any Coxeter group,we define rigid reflections and rigid roots using non-self-intersecting curves on a Riemann surface with labeled curves.When the Coxeter group arises from an acyclic quiver,they are related to the rigid representations of the quiver.For a family of rank 3 Coxeter groups,we show that there is a surjective map from the set of reduced positive roots of a rank 2 Kac-Moody algebra onto the set of rigid reflections.We conjecture that this map is bijective.