https://doi.org/10.1140/epjc/s10052-024-13040-w
Regular Article - Theoretical Physics
Generalized 
and (q, t)-deformed partition functions with W-representations and Nekrasov partition functions
1
School of Mathematical Sciences, Capital Normal University, 100048, Beijing, China
2
Department of Mathematics, China University of Mining and Technology, 100083, Beijing, China
Received:
4
June
2024
Accepted:
24
June
2024
Published online:
29
July
2024
We construct the generalized 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 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.
© The Author(s) 2024
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