Rigid reflections and Kac--Moody algebras
Representation Theory
2018-03-15 v1 Combinatorics
Rings and Algebras
Abstract
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.
Cite
@article{arxiv.1803.05373,
title = {Rigid reflections and Kac--Moody algebras},
author = {Kyu-Hwan Lee and Kyungyong Lee},
journal= {arXiv preprint arXiv:1803.05373},
year = {2018}
}