2022/05/14 by Grantcharov, Dimitar, Penkov, Ivan, Serganova, Vera · 2 citations
#17B10 #17B65 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2205.07138
We classify simple bounded weight modules over the complex simple Lie superalgebras \mathfraksl(∞ |∞) and \mathfrakosp (m | 2n), when at least one of m and n equals ∞. For \mathfrakosp (m | 2n) such modules are of spinor-oscillator type, i.e., they combine into one the known classes of spinor \mathfrako (m)-modules and oscillator-type \mathfraksp (2n)-modules. In addition, we characterize the category of bounded weight modules over \mathfrakosp (m | 2n) (under the assumption dim \mathfrakosp (m | 2n) = ∞) by reducing its study to already known categories of representations of \mathfraksp (2n), where n possibly equals ∞. When classifying simple bounded weight \mathfraksl(∞ |∞)-modules, we prove that every such module is integrable over one of the two infinite-dimensional ideals of the Lie algebra \mathfraksl(∞ |∞)_0. We finish the paper by establishing some first facts about the category of bounded weight \mathfraksl (∞ |∞)-modules.