Infinite rank module categories over finite dimensional \mathfraksl₂-modules in Lie-algebraic context

2024/05/30 by Volodymyr Mazorchuk, Mazorchuk, Volodymyr, Xiaoyu Zhu +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2405.19894

openalex publication_date 2024/05/30 · openalex created_date 2024/06/01 · openalex updated_date 2026/07/28

Abstract

We study locally finitary realizations of simple transitive module categories of infinite rank over the monoidal category \mathscrC of finite dimensional modules for the complex Lie algebra \mathfraksl₂. Combinatorics of such realizations is governed by six infinite Coxeter diagrams. We show that five of these are realizable in our setup, while one (type B_∞) is not. We also describe the \mathscrC-module subcategories of \mathfraksl₂-mod generated by simple modules as well as the \mathscrC-module categories coming from the natural action of \mathscrC on the categories of finite dimensional modules over Lie subalgebras of \mathfraksl₂.

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