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

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.

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Publication Details

Journal
Theoretical and Mathematical Physics
Published
2025-12-01
DOI
https://doi.org/10.1134/s0040577925120049
Primary Topic
Algebraic structures and combinatorial models
Type
article
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article

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

Chuanzhong Li, A. D. Mironov, A. Yu. Orlov
Theoretical and Mathematical Physics
Algebraic structures and combinatorial models
article

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

Chuanzhong Li, A. D. Mironov, A. Yu. Orlov
article en

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.

Theoretical and Mathematical PhysicsVol. 225(3)
National Research University Higher School of Economics (RU), P.N. Lebedev Physical Institute of the Russian Academy of Sciences (RU), Institute of Oceanology. PP Shirshov Russian Academy of Sciences (RU), Kurchatov Institute (RU), Institute for Information Transmission Problems (RU), Shandong University of Science and Technology (CN)
Reduced inequalities
Openalex Percentile: Top 22%
Algebraic structures and combinatorial models
DOISourceOpenAlex
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Tau functions of the UC hierarchy as partition functions of matrix models — Chuanzhong Li, A. D. Mironov, et al. · Theoretical and Mathematical Physics (2025) | TGRS Research Map | TGRS