Generalized $β$ and $(q,t)$-deformed partition functions with $W$-representations and Nekrasov partition functions
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| Format: | Preprint |
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2024
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| _version_ | 1866929443613704192 |
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| author | Liu, Fan Wang, Rui Yang, Jie Zhao, Wei-Zhong |
| author_facet | Liu, Fan Wang, Rui Yang, Jie Zhao, Wei-Zhong |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_11970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized $β$ and $(q,t)$-deformed partition functions with $W$-representations and Nekrasov partition functions Liu, Fan Wang, Rui Yang, Jie Zhao, Wei-Zhong High Energy Physics - Theory Mathematical Physics 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. |
| title | Generalized $β$ and $(q,t)$-deformed partition functions with $W$-representations and Nekrasov partition functions |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2405.11970 |