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arXiv · 2206.13038

Superintegrability for ($\beta$-deformed) partition function hierarchies with $W$-representations

Rui Wang·Fan Liu·Chun-Hong Zhang·Wei-Zhong Zhao
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Abstract

We construct the ($\beta$-deformed) partition function hierarchies with $W$-representations. Based on the $W$-representations, we analyze the superintegrability property and derive their character expansions with respect to the Schur functions and Jack polynomials, respectively. Some well known superintegrable matrix models such as the Gaussian hermitian one-matrix model (in the external field), $N\times N$ complex matrix model, $\beta$-deformed Gaussian hermitian and rectangular complex matrix models are contained in the constructed hierarchies.

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Rui Wang, Fan Liu, Chun-Hong Zhang, Wei-Zhong Zhao. 2022-06-27. Superintegrability for ($\beta$-deformed) partition function hierarchies with $W$-representations. https://doi.org/10.1140/epjc%2Fs10052-022-10875-z

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