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arXiv · 2510.22877

Generalized permutation matrices and non-weight modules over $\mathfrak{sl}(m|1)$

Ivan Dimitrov·Khoa Nguyen·Charles Paquette·David Wehlau
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Abstract

We study the category $\mathcal{M}_{\mathfrak{sl}(m|1)}(k|k)$ of $\mathcal U(\mathfrak h)\text{-free}$ $\mathcal U(\mathfrak{sl}(m|1))$-modules of rank $k$ in each parity (rank $(k|k)$), where $k\in\mathbb{Z}_{\geq1}$. We construct an explicit family of such modules, provide an isomorphism theorem, and establish an indecomposability criterion.

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Ivan Dimitrov, Khoa Nguyen, Charles Paquette, David Wehlau. 2025-10-27. Generalized permutation matrices and non-weight modules over $\mathfrak{sl}(m|1)$. https://arxiv.org/abs/2510.22877

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