On the slopes of semistable representations of tame quivers

TL;DR

This paper investigates the slopes of semistable representations of tame quivers under fixed stability conditions, providing a detailed description relevant to the understanding of quiver representations.

Contribution

It offers a new characterization of slopes of semistable representations specifically for tame quivers, enhancing the understanding of their stability properties.

Findings

Explicit description of slopes for semistable representations

Application to classification of tame quiver representations

Insights into stability conditions in representation theory

Abstract

Stability conditions play an important role in the study of representations of a quiver. In the present paper, we study semistable representations of quivers. In particular, we describe the slopes of semistable representations of a tame quiver for a fixed stability condition.