A spin analog of the plethystic Murnaghan-Nakayama rule

As a spin analog of the plethystic Murnaghan-Nakayama rule for Schur functions, the plethystic Murnaghan-Nakayama rule for Schur $Q$-functions is established with the help of the vertex operator realization. This generalizes both the Murnaghan-Nakayama rule and the Pieri rule for Schur $Q$-functions. A plethystic Murnaghan-Nakayama rule for Hall-Littlewood functions is also investigated.