Diagrammatic Categories which arise from Representation Graphs

Abstract

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 $G-\text{mod}$ with objects being the tensor products of finitely many irreducible $G$-modules.