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arXiv · 2603.04303

Simple $\mathfrak{sl}_2$-modules that are torsion free $U(\mathfrak{h})$-modules of rank $1$

Dimitar Grantcharov·Libor Krizka·Volodymyr Mazorchuk
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Abstract

We provide an explicit classification of all simple $\mathfrak{sl}_2$-modules that are torsion free of rank $1$ over the Cartan subalgebra. We also establish a similar result for the first Weyl algebra and for the Lie superalgebra $\mathfrak{osp}(1|2)$.

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Dimitar Grantcharov, Libor Krizka, Volodymyr Mazorchuk. 2026-03-04. Simple $\mathfrak{sl}_2$-modules that are torsion free $U(\mathfrak{h})$-modules of rank $1$. https://arxiv.org/abs/2603.04303

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