Skew quantum Murnaghan–Nakayama rule

Abstract

We extend recent results of Assaf and McNamara on a skew Pieri rule and a skew Murnaghan---Nakayama rule to a more general identity, which gives an elegant expansion of the product of a skew Schur function with a quantum power sum function in terms of skew Schur functions. We give two proofs, one completely bijective in the spirit of Assaf---McNamara's original proof, and one via Lam---Lauve---Sotille's skew Littlewood---Richardson rule. We end with some conjectures for skew rules for Hall---Littlewood polynomials.