Supersymmetric partition function hierarchies and character expansions

Abstract

We construct the supersymmetric $$\beta $$ 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 $$\beta $$ β and (q, t)-deformed superoperators, we further give the supersymmetric $$\beta $$ 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., $$<character>\sim character$$ < c h a r a c t e r > ∼ c h a r a c t e r .