On $U(\mathfrak{h})$-free modules of finite rank over $\mathfrak{sl}(2)$

Dimitar Grantcharov; Khoa Nguyen; Kaiming Zhao

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arXiv · 2606.28096

On $U(\mathfrak{h})$-free modules of finite rank over $\mathfrak{sl}(2)$

Dimitar Grantcharov·Khoa Nguyen·Kaiming Zhao

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Abstract

We study $\mathfrak{sl}(2)$-modules that are free of finite rank over $U(\mathfrak h)$, where $\mathfrak h$ is a fixed Cartan subalgebra of $\mathfrak{sl}(2)$. These modules form a natural class of non-weight modules. The coherent families obtained from this class via the weighting functor are identified. We also study a distinguished class of indecomposable $U(\mathfrak h)$-free modules defined in terms of Jordan blocks and give a recursive description of their socle filtrations. Finally, we apply the general results to exponential modules arising from the first Weyl algebra and obtain simplicity criteria for these modules.

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BibTeX RIS

Dimitar Grantcharov, Khoa Nguyen, Kaiming Zhao. 2026-06-26. On $U(\mathfrak{h})$-free modules of finite rank over $\mathfrak{sl}(2)$. https://arxiv.org/abs/2606.28096

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