Interpolating matrix models for WLZZ series
А. Миронов, V. Mishnyakov, A. Morozov, A. Popolitov, Rui Wang, Weizhong Zhao
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 $$w_\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>w</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:math> -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 $$\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math> -functions.