Interpolating matrix models for WLZZ series

Abstract

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 $$w_\infty $$ 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 $$\tau $$ τ -functions.