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Abstract <p> We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. We find new matrix models associated with the product of two spheres with embedded graphs via a gluing matrix. We also generalize these studies to the multi-matrix model case, which corresponds to the multi-component UC hierarchy. </p>

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Tau functions of the UC hierarchy as partition functions of matrix models

  • 期刊论文

  • 发表日期：

    2025年12月23日

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  • Chuanzhong Li,
  • A. D. Mironov,
  • A. Yu. Orlov

摘要

Abstract

We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. We find new matrix models associated with the product of two spheres with embedded graphs via a gluing matrix. We also generalize these studies to the multi-matrix model case, which corresponds to the multi-component UC hierarchy.