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arXiv · 2208.03671

Supersymmetric partition function hierarchies and character expansions

Rui Wang·Fan Liu·Min-Li Li·Wei-Zhong Zhao
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Abstract

We construct the supersymmetric $\beta$ and $(q,t)$-deformed Hurwitz-Kontsevich partition functions through $W$-representations and present the corresponding character expansions with respect to the Jack and Macdonald superpolynomials, respectively. Based on the constructed $\beta$ and $(q,t)$-deformed superoperators, we further give the supersymmetric $\beta$ and $(q,t)$-deformed partition function hierarchies through $W$-representations. We also present the generalized super Virasoro constraints, where the constraint operators obey the generalized super Virasoro algebra and null super 3-algebra. Moreover, the superintegrability for these (non-deformed) supersymmetric hierarchies is shown by their character expansions, i.e., $ \sim character$.

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Rui Wang, Fan Liu, Min-Li Li, Wei-Zhong Zhao. 2022-08-07. Supersymmetric partition function hierarchies and character expansions. https://arxiv.org/abs/2208.03671

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