Diagrammatic Categories which arise from Representation Graphs

2025/02/07 by Reynolds, Ryan
Computer Science · #Category Theory (math.CT) #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #Data Management and Algorithms #Digital Image Processing Techniques #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2502.05005

openalex publication_date 2025/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 Dgrams_R(V,G) and a full subcategory of G-mod with objects being the tensor products of finitely many irreducible G-modules.

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