Representations of quantum toroidal superalgebras and plane s-partitions

Abstract

We construct Fock and MacMahon modules for the quantum toroidal superalgebra [Formula: see text] associated with the Lie superalgebra [Formula: see text] and parity [Formula: see text]. 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 [Formula: see text] is given by Pieri-type formulas. We study the corresponding characters.