In [1973 paper](http://www.math.tau.ac.il/~bernstei/Publication_list/publication_texts/BGG-CoxeterF-Usp.pdf) about Gabriel's theorem, there is an open question:


Suppose we have a graph $\Gamma$ and two orientations $\Lambda,\Lambda'$ of it. Then for each indecomposable representation of $\Lambda$ there is an indecomposable representation of $\Lambda'$ with the same diensional vector.


Is this question still open? Maybe there is some analogue of reflection functor not only for sinks and sources?



Connection between representations of different orientations of graph
In the paper 


V.G. Kac, "Infinite root systems, representations of graphs and invariant theory", Invent. Math. 56, 57-92 (1980), 


Kac shows that the dimension vectors of indecomposable representations are (independently of the orientation) the positive roots of a Kac-Moody Lie algebra.


Actually, his original statement assumes that the quiver has no loops, but quivers with loops are covered as well in


V.G. Kac, "Root systems, representations of quivers and invariant theory" in *Invariant Theory* (ed. F. Gherardelli) LNM 996 (Springer, 1983), pp 74-108. 


