  We investigate representations of *-algebras associated with posets.
Unitarizable representations of the corresponding (bound) quivers (which are
polystable representations for some appropriately chosen slope function) give
rise to representations of these algebras. Considering posets which correspond
to unbound quivers this leads to an ADE-classification which describes the
unitarization behaviour of their representations. Considering posets which
correspond to bound quivers, it is possible to construct unitarizable
representations starting with polystable representations of related unbound
quivers which can be glued together with a suitable direct sum of simple
representations. Finally, we estimate the number of complex parameters
parametrizing irreducible unitary non-equivalent representations of the
corresponding algebras.
