Interpolating matrix models for WLZZ series

Abstract

AbstractWe 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 throughW-representations. We also discuss further generalizations of the WLZZ models, realized byW-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.