Representations of Bisected Posets and Reflection Functors

We construct a complete set of reflection functors for the representations of posets and prove that they really have the usual properties. In particular, when the poset is of finite representation type, all its indecomposable representations can be obtained from some "trivial" ones via reflections. To define such reflection functors, a wider class of matrix problem is introduced, called "representations of bisected posets". Representations of partially ordered sets ("posets") introduced by Nazarova and Roiter [7] were, maybe, the first example of matrix problems, whose theory was circumstantially elaborated. Later on they played an eminent role in the whole theory of matrix problems as well as of representations of algebras. So it is not surprising that it was also the first case, when one tried to introduce something like Bernstein--Gelfand--Ponomarev's reflection functors. Namely, one could not define all of them though in [2] the author managed to introduce some substitutes for one..