Supersymmetric partition function hierarchies and character expansions

We construct the supersymmetric β and ( q , t )-deformed Hurwitz–Kontsevich partition functions through W -representations and present the corresponding character expansions with respect to the Jack and Macdonald superpolynomials, respectively. Based on the constructed β and ( q , t )-deformed superoperators, we further give the supersymmetric β and ( q , t )-deformed partition function hierarchies through W -representations. We also present the generalized super Virasoro constraints, where the constraint operators obey the generalized super Virasoro algebra and null super 3-algebra. Moreover, the superintegrability for these (non-deformed) supersymmetric hierarchies is shown by their character expansions, i.e., ∼ character .