Representations of quantum toroidal superalgebras and plane s-partitions (Q6634055)

This paper studies the representation theory of quantum toroidal superalgebras \(\mathcal{E}_s\) associated with the Lie superalgebra \(\mathfrak{gl}_{m|n}\) and parity \(\mathbf{s}\), where \(m\ne n\) which were introduced by the authors in a previous paper. They study the modules in a different way from a previous work by the same authors. This formulation is given in terms of combinatorics of partitions, plane partitions, and their supersymmetric analogs. For the construction they follow the paper by \textit{B. Feigin} et al. [J. Algebra 380, 78--108 (2013; Zbl 1293.17017)], but they made several modifications to cover the supersymmetric case. They construct Fock and MacMahon modules for \(\mathcal{E}_s\).