A new algebraic structure encodes symmetry rules for super Macdonald polynomials

Super Macdonald polynomials—a supersymmetric generalization of classical Macdonald polynomials indexed by super partitions—form a natural basis for a representation of the quantum toroidal algebra associated with the superalgebra gl(1|1). By analyzing how supercharge operators act on this space, the authors derive Pieri rules: explicit formulas for multiplying a super Macdonald polynomial by a single-variable symmetric function. These rules translate into differential operators on a combined boson-fermion Fock space, and anti-commutators of the supercharges reproduce known supersymmetric Hamiltonians. A notable technical finding is that the relevant algebraic structure requires a shifted, rather than standard, quantum toroidal algebra.