Combinatorics of infinite rank module categories over finite dimensional $\mathfrak{sl}_3$-modules in Lie-algebraic context

Volodymyr Mazorchuk; Xiaoyu Zhu

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arXiv · 2501.00291

Combinatorics of infinite rank module categories over finite dimensional $\mathfrak{sl}_3$-modules in Lie-algebraic context

Volodymyr Mazorchuk·Xiaoyu Zhu

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Abstract

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.

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BibTeX RIS

Volodymyr Mazorchuk, Xiaoyu Zhu. 2024-12-31. Combinatorics of infinite rank module categories over finite dimensional $\mathfrak{sl}_3$-modules in Lie-algebraic context. https://arxiv.org/abs/2501.00291

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