Shifted quantum toroidal algebra of type ${\mathfrak{gl}}_{1|1}$ and the Pieri rule of the super Macdonald polynomials

Hiroaki Kanno, Ryo Ohkawa, Jun'ichi Shiraishi

The super Macdonald polynomials indexed by the super partitions form a basis of the level zero super Fock module (combinatorial representation) of the quantum toroidal algebra $\ma…