Shift orbits for elementary representations of Kronecker quivers

Abstract Let . We denote by the wild ‐Kronecker quiver with arrows and consider the action of the group generated by and on the set of regular dimension vectors A fundamental domain of this action is given by . We classify the subset of dimension vectors of elementary representations. Moreover, given , we show that the set of elementary representations with dimension vector is a dense open subset in the irreducible variety of representations. A complete combinatorial description of elementary representations for has been given by Ringel. We show that such a compact description is out of reach when we consider , although the representation theory of is as difficult as the representation theory of for .