Interpolating matrix models for WLZZ series

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 asso-ciated with infinite commutative families of generators of w8-algebra which are presumably related to more sophis-ticated multi-matrix models. Integrable properties of these generalizations are described by what we call the skew hyper-geometric t-functions.

Automated summary

We propose a two-matrix model with three sets of parameters that can interpolate between various models. These models are defined through W-representations and have integrable properties described by skew hyper-geometric t-functions. We also discuss generalizations of the WLZZ models realized by W-representations associated with infinite commutative families of generators of w8-algebra.