Stable representations of posets

The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a poset of finite type is stable with respect to some weight and construct that weight explicitly in terms of the dimension vector. We show that if a poset is primitive then Coxeter transformations preserve stable representations. When the base field is the field of complex numbers we establish the connection between the polystable representations and the unitary $\chi$-representations of posets. This connection explains the similarity of the results obtained in the series of papers.