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

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 $k\in {\mathbb{Z}}_{\ge 1}$. We construct an explicit family of such modules, provide an isomorphism theorem, and establish an indecomposability criterion.

42 pages