ABSTRACT
This chapter is devoted to finite partially ordered sets and their representations, which play an important role in representation theory in general. Representations of posets were first introduced and studied by L. A. Nazarova and A. V. Roiter in 1972 in connection with problems of representations of finite dimensional algebras. This chapter gives the proof of a criterium for primitive posets to be of finite representation type. As for one poset, one can introduce the notion of a direct sum of matrix representations of a pair of posets, and the notion of an indecomposable matrix representation. This chapter deals with the necessity part of the theorem 5.6.1, i.e. it proves that all critical primitive posets from theorem are of infinite representation type.
