On the combinatorial nature of tree representations of Euclidean quivers

Abstract

We verify computationally a conjecture on the field independence of tree representations of Euclidean quivers, with dimension vector bounded by the minimal radical vector of the quiver. This includes a large class of exceptional representations, in particular all the regular non-homogeneous exceptionals. In addition we also present some thought-provoking findings, which further confirms the combinatorial nature of the category of representations of tame quivers.