Exponential modules of \mathfrakosp(1|2)

2025/10/31 by Grantcharov, Dimitar, Nguyen, Khoa
#17A70 #17B10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.00287

Abstract

We study properties of two families, E₊(g) and E_-(g), of non-weight modules over the orthosymplectic Lie superalgebra \mathfrakosp(1|2) that are parameterized by a nonconstant polynomial g(x) ∈ \mathbb C [x]. These families appear naturally from the two oscillator homomorphisms and the exponential modules over the first Weyl algebra \mathcal D(1). We prove simplicity and isomorphism theorems for E₊(g) and E_-(g).

Citations

• Bounded weight modules for basic classical Lie superalgebras at infinity
• Construction of simple non-weight sl(2)-modules of arbitrary rank

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