Admissible sequences and the preprojective component of a quiver

This paper concerns indecomposable preprojective modules over the path algebra of a finite connected quiver without oriented cycles. For each such module, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the module. An efficient way to compute the module is to recover it from its shortest (+)-admissible sequence. The set of equivalence classes of the above sequences has a natural structure of a partially ordered set. For a large class of quivers, the Hasse diagram of the partially ordered set is isomorphic to the preprojective component of the Auslander-Reiten quiver. The techniques of (+)-admissible sequences yield a new result about slices in the preprojective component.