Diagrammatic Categories which arise from Representation Graphs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912223578816512 |
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| author | Reynolds, Ryan |
| author_facet | Reynolds, Ryan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05005 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diagrammatic Categories which arise from Representation Graphs Reynolds, Ryan Category Theory Combinatorics Representation Theory 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. |
| title | Diagrammatic Categories which arise from Representation Graphs |
| topic | Category Theory Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2502.05005 |