The main result of this paper utilizes the representation graph of a group $G$, $R(V,G)$, and gives a general construction of a diagrammatic category $\mathbf{ Dgrams}_{ R(V,G)}$. The proof of the main theorem shows that, given explicit criteria, there is an equivalence of categories between a quotient category of $\mathbf{ Dgrams}_{ R(V,G)}$ and a full subcategory of $G-\textbf{ mod}$ with objects being the tensor products of finitely many irreducible $G$-modules.
Categories: math.CT math.CO math.RT