Tau functions of the UC hierarchy as partition functions of matrix models
arXiv:2506.12867 · doi:10.4213/tmf10973
Abstract
We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. This develops one of the topics of our previous paper arXiv:2410.14823. We found new matrix models associated with the product of two spheres with embedded graphs via a gluing matrix. We also generalize these studies to multi-matrix models case, which corresponds to the multi-component UC hierarchy.
22 pages, 6 figures
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