Diagrammatic Categories which arise from Representation Graphs

Ryan Reynolds

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arXiv · 2502.05005

Diagrammatic Categories which arise from Representation Graphs

Ryan Reynolds

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

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Ryan Reynolds. 2025-02-07. Diagrammatic Categories which arise from Representation Graphs. https://arxiv.org/abs/2502.05005

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