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arXiv · 2304.03051

Matrix models for the nested hypergeometric tau-functions

Alexander Alexandrov
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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.

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Alexander Alexandrov. 2023-04-06. Matrix models for the nested hypergeometric tau-functions. https://doi.org/10.4310/cntp.250531024251

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