Super Macdonald polynomials indexed by super partitions form a basis of the level zero super Fock module of the shifted quantum toroidal algebra U_{q,t}(gl hat hat 1|1), with the Pieri rule following from super charge actions and yielding supersymmetric Hamiltonians via anti-commutators.
Shifted quiver quantum toroidal algebra and sub- crystal representations,
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Shifted quantum toroidal algebra of type $\mathfrak{gl}_{1|1}$ and the Pieri rule of the super Macdonald polynomials
Super Macdonald polynomials indexed by super partitions form a basis of the level zero super Fock module of the shifted quantum toroidal algebra U_{q,t}(gl hat hat 1|1), with the Pieri rule following from super charge actions and yielding supersymmetric Hamiltonians via anti-commutators.