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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.14501 |
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| _version_ | 1866908832422166528 |
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| author | Le, Ian Yıldırım, Emine |
| author_facet | Le, Ian Yıldırım, Emine |
| contents | The homogeneous coordinate ring of the Grassmannian $\rm{Gr}(k,n)$ has a well-known cluster structure. There is a categorification of this cluster structure via a category of modules for a ring $A_{k,n}$ due to Jensen-King-Su, building on work of Geiss-Leclerc-Schröer, in which cluster variables correspond to indecomposable rigid modules. We give a combinatorial description of modules that correspond to rank $2$ cluster variables by using webs. This conjecturally gives the categorification of all rank $2$ cluster variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cluster Categorification of Rank 2 Webs Le, Ian Yıldırım, Emine Representation Theory Combinatorics 13F60, 16G20, 14M15 The homogeneous coordinate ring of the Grassmannian $\rm{Gr}(k,n)$ has a well-known cluster structure. There is a categorification of this cluster structure via a category of modules for a ring $A_{k,n}$ due to Jensen-King-Su, building on work of Geiss-Leclerc-Schröer, in which cluster variables correspond to indecomposable rigid modules. We give a combinatorial description of modules that correspond to rank $2$ cluster variables by using webs. This conjecturally gives the categorification of all rank $2$ cluster variables. |
| title | Cluster Categorification of Rank 2 Webs |
| topic | Representation Theory Combinatorics 13F60, 16G20, 14M15 |
| url | https://arxiv.org/abs/2402.14501 |