Phases of stable representations of quivers

TL;DR

This paper investigates the behavior of stable quiver representations, showing that under certain conditions, their phases cluster around specific points and are not densely distributed.

Contribution

It establishes a link between the existence of stable representations with self-extensions and the accumulation of phases of stable representations.

Findings

Phases of stable representations approach one or two limit points.

Phases are not dense in two arcs.

Existence of a stable with self-extensions implies infinitely many without.

Abstract

We consider stable representations of non-Dynkin quivers with respect to a central charge. On one condition the existence of a stable representation with self-extensions implies the existence of infinitely many stables without self-extensions. In this case the phases of the stable representations approach one or two limit points. In particular, the phases are not dense in two arcs.