Interpolating matrix models for WLZZ series

Abstract We suggest a two-matrix model depending on three (infinite) sets of parameters which interpolates between all the models proposed in Wang et al. (Eur Phys J C 82: 902, arXiv: 2206. 13038, 2022) and defined there through W -representations. We also discuss further generalizations of the WLZZ models, realized by W -representations associated with infinite commutative families of generators of w_ w∞ -algebra which are presumably related to more sophisticated multi-matrix models. Integrable properties of these generalizations are described by what we call the skew hypergeometric τ -functions.