Simple weight modules over the quantum Schrödinger algebra

2017/04/05 by Yan-an Cai, Cai, Yan-an, Yongsheng Cheng +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1704.01393

openalex publication_date 2017/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, using the technique of localization, we determine the center of the quantum Schrödinger algebra §_q and classify simple modules with finite-dimensional weight spaces over §_q, when q is not a root of unity. It turns out that there are four classes of such modules: dense U_q(\mathfraksl₂)-modules, highest weight modules, lowest weight modules, and twisted modules of highest weight modules.

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