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arXiv · 2301.12763

$W$-representations for multi-character partition functions and their $β$-deformations

Lu-Yao Wang·V. Mishnyakov·A. Popolitov·Fan Liu·Rui Wang
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Abstract

In this letter we continue the development of $W$-representations. We propose several generalizations of the known models, such as the hypergeometric Hurwitz $τ$-functions. We construct $W$-representations for multi-character expansions, which involve a generic number of sets of time variables. We propose integral representations for such kind of partition functions which are given by tensor models and multi-matrix models with multi-trace couplings. We further propose the $β$-deformation of the discussed $W$-representation for the Hurwitz case for two sets of times as well as for the multi-character case.

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Lu-Yao Wang, V. Mishnyakov, A. Popolitov, Fan Liu, Rui Wang. 2023-01-31. $W$-representations for multi-character partition functions and their $β$-deformations. https://arxiv.org/abs/2301.12763

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