Rigid reflections and Kac--Moody algebras

2018/03/14 by Lee, Kyu-Hwan, Lee, Kyungyong
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1803.05373

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.

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