2015/09/16 by Oh, Se-Jin, Suh, Uhi Rinn · 1 citation
#16T30 #17B37 #5E10 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1509.04820
In this paper, we introduce the notion of combinatorial Auslander-Reiten(AR) quiver for commutation classes [\widetildew] of w in finite Weyl group. This combinatorial object visualizes the convex partial order \prec_[\widetildew] on the subset Φ(w) of positive roots. By analyzing properties of the combinatorial AR-quivers with labelings and reflection maps, we can apply their properties to the representation theory of KLR algebras and multiplication structure of dual PBW generators associated to any commutation class [\widetildew0] of the longest element w0.