2022/07/10 by Yikun Zhou, Zhou, Yikun, Yilan Tan +3
Mathematics · #20G42 #81R50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2207.04432
openalex publication_date 2022/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathfrakg be a finite-dimensional simple Lie algebra over ℂ. A Y(\mathfrakg)-module is said to be weight if it is a weight \mathfrakg-module. We give a complete classification of simple weight modules for Y(\mathfraksl2) which admits a one-dimensional weight space. We prove that there are four classes of such modules: finite, highest weight, lowest weight and dense modules. Different from the classical \mathfraksl2 representation theory, we show that there exist a class of Y(\mathfraksl2) irreducible modules which have uniformly 2-dimensional weight spaces.