We present a general scheme for describing ŝu(N)k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its Berenstein-Zelevinsky triangle) and the threshold level at which it first appears. We show that a closed expression for this threshold level is encoded in the Berenstein-Z...

So far few theoretical works investigated the conditions under which specific fusion rules can work well, and a unifying framework for comparing rules of different complexity is clearly beyond the state of the art. A clear theoretical comparison is lacking even if one focuses on specific classes of combiners (e.g., linear combiners). In this paper, we theoretically compare simple and weighted a...