Generalized $β$ and $(q,t)$-deformed partition functions with $W$-representations and Nekrasov partition functions Article Swipe

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Fan Liu , Rui Wang , Jie Yang , Wei‐Zhong Zhao · YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2405.11970

We construct the generalized $β$ and $(q,t)$-deformed partition functions through $W$ representations, where the expansions are respectively with respect to the generalized Jack and Macdonald polynomials labeled by $N$-tuple of Young diagrams. We find that there are the profound interrelations between our deformed partition functions and the $4d$ and $5d$ Nekrasov partition functions. Since the corresponding Nekrasov partition functions can be given by vertex operators, the remarkable connection between our $β$ and $(q,t)$-deformed $W$-operators and vertex operators is revealed in this paper. In addition, we investigate the higher Hamiltonians for the generalized Jack and Macdonald polynomials.

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/2405.11970

PDF

https://arxiv.org/pdf/2405.11970

OA Status

green

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10

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https://openalex.org/W4398192453

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