Combinatorics of infinite rank module categories over finite dimensional $\mathfrak{sl}_3$-modules in Lie-algebraic context
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909445902041088 |
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| author | Mazorchuk, Volodymyr Zhu, Xiaoyu |
| author_facet | Mazorchuk, Volodymyr Zhu, Xiaoyu |
| contents | We determine the combinatorics of transitive module categories over the monoidal category of finite dimensional $\mathfrak{sl}_3$-modules which arise when acting by the latter monoidal category on arbitrary simple $\mathfrak{sl}_3$-modules. This gives us a family of eight graphs which can be viewed as $\mathfrak{sl}_3$-generalizations of the classical infinite Dynkin diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorics of infinite rank module categories over finite dimensional $\mathfrak{sl}_3$-modules in Lie-algebraic context Mazorchuk, Volodymyr Zhu, Xiaoyu Representation Theory We determine the combinatorics of transitive module categories over the monoidal category of finite dimensional $\mathfrak{sl}_3$-modules which arise when acting by the latter monoidal category on arbitrary simple $\mathfrak{sl}_3$-modules. This gives us a family of eight graphs which can be viewed as $\mathfrak{sl}_3$-generalizations of the classical infinite Dynkin diagrams. |
| title | Combinatorics of infinite rank module categories over finite dimensional $\mathfrak{sl}_3$-modules in Lie-algebraic context |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2501.00291 |