Matrix models for the nested hypergeometric tau-functions

Abstract

We introduce and investigate a family of tau-functions of the 2D Toda hierarchy, which is a natural generalization of the hypergeometric family associated with Hurwitz numbers. For this family we prove a skew Schur function expansion formula. For arbitrary rational weight generating functions we construct the multi-matrix models. Two different types of cut-and-join descriptions are derived. Considered examples include generalized fully simple maps, which we identify with the recently introduced skew hypergeometric tau-functions.