Total stability functions for type \mathbbA quivers

2020/02/27 by Kinser, Ryan
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2002.12396

Abstract

For a quiver Q of Dynkin type \mathbbA_n, we give a set of n-1 inequalities which are necessary and sufficient for a linear stability condition (a.k.a. central charge) Z\colon K₀(Q) → ℂ to make all indecomposable representations stable. We furthermore show that these are a minimal set of inequalities defining the space TS(Q) of total stability conditions, considered as an open subset of ℝ^Q₀ × (ℝ_>0)^Q₀. We then use these inequalities to show that each fiber of the projection of TS(Q) to (ℝ_>0)^Q₀ is linearly equivalent to ℝ × ℝ_>0^Q₁.

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