2022/08/04 by Diaz, Yariana, Gilbert, Cody, Kinser, Ryan
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2208.02445
This paper concerns stability functions for Dynkin quivers, in the generality introduced by Rudakov. We show that relatively few inequalities need to be satisfied for a stability function to be totally stable (i.e. to make every indecomposable stable). Namely, a stability function μ is totally stable if and only if μ(τV) < μ(V) for every almost split sequence 0 → τV → E → V → 0 where E is indecomposable. These can be visualized as those sequences around the "border" of the Auslander-Reiten quiver.