Total Stability Functions for Type A Quivers.

For a quiver Q of Dynkin type A 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 : K 0 (Q) → ℂ to make all indecomposable representations stable. We furthermore show that these are a minimal set of inequalities defining the space T S (Q) of total stability conditions, considered as an open subset of ℝ Q 0 × (ℝ > 0) Q 0 . We then use these inequalities to show that each fiber of the projection of T S (Q) to (ℝ > 0) Q 0 is linearly equivalent to ℝ × ℝ > 0 Q 1 . [ABSTRACT FROM AUTHOR]