Generalized $\beta$ and $(q,t)$-deformed partition functions with
$W$-representations and Nekrasov partition functions
Generalized $\beta$ and $(q,t)$-deformed partition functions with
$W$-representations and Nekrasov partition functions
We construct the generalized $\beta$ 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 $5d$ …