Representations of quantum toroidal superalgebras and plane $\mathbf{s}$-partitions

Abstract

We construct Fock and MacMahon modules for the quantum toroidal superalgebra ${\mathcal{E}}_{\mathbf{s}}$ associated with the Lie superalgebra ${\mathfrak{gl}}_{m|n}$ and parity $\mathbf{s}$. The bases of the Fock and MacMahon modules are labeled by super-analogs of partitions and plane partitions with various boundary conditions, while the action of generators of ${\mathcal{E}}_{\mathbf{s}}$ is given by Pieri type formulas. We study the corresponding characters.

v1: Latex, 42 pages, 14 figures. v2: minor corrections. Comments are welcome!

References in corpus (1)

• Crystal Melting and Toric Calabi-Yau Manifolds

Cited by in corpus (1)

• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations