The University of Michigan Combinatorics Seminar
A quiver is just a directed graph. If we attach vector spaces to the vertices and linear maps to the arrows (with the apropiate domain and co-domain) then we get a representation of that quiver. The classical Bernstein-Gelfand-Ponomarev reflection functors for quiver representations are defined for vertices which are sinks or sources. We will generalize these reflections to arbitrary vertices. For this, it seems that one needs to study quivers with potentials. Quivers with potentials and their representations are closely related to cluster algebras introduced by Fomin and Zelevinsky. Indeed, this is one of the main motivations to study them. This is joint work with Jerzy Weyman and Andrei Zelevinsky.