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Mutations of reflections and existence of pseudo-acyclic orderings for type
Tucker J. Ervin, Blake Jackson, Kyu-Hwan Lee +1
In a recent paper by K.-H. Lee, K. Lee and M. Mills, a mutation of reflections in the universal Coxeter group is defined in association with a mutation of a quiver. A matrix repres…
Rigid reflections and Kac--Moody algebras
Kyu-Hwan Lee, Kyungyong Lee
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…
A correspondence between rigid modules over path algebras and simple curves on Riemann surfaces
Kyu-Hwan Lee, Kyungyong Lee
We propose a conjectural correspondence between the set of rigid indecomposable modules over the path algebras of acyclic quivers and the set of certain non-self-intersecting curve…
A combinatorial approach to root multiplicities of rank 2 hyperbolic Kac-Moody algebras
Seok-Jin Kang, Kyu-Hwan Lee, Kyungyong Lee
In this paper we study root multiplicities of rank 2 hyperbolic Kac-Moody algebras using the combinatorics of Dyck paths.