Title: Stable representations of posets,
Abstract: 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.