On the slopes of semistable representations of tame quivers

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.

KEYWORDS:

• Slope
• stability condition
• tame quiver

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16G20
• 16G70

Acknowledgments

We are very grateful to Professor Bangming Deng for his encouragement and careful guidance. We thank Shiquan Ruan, Qinghua Chen, and Jie Zhang for many helpful discussions. We are also grateful to Magnus Engenhorst for pointing out to us the reference [8].