On numerators of bigraded symmetric orbifold Hilbert series and
$q,t$-Kostka Macdonald polynomials
On numerators of bigraded symmetric orbifold Hilbert series and
$q,t$-Kostka Macdonald polynomials
We show that the numerators of bigraded symmetric orbifold Hilbert series are the (transpose of the) matrix of $q,t$-Kostka Macdonald coefficients $K_d = \left( K_{\lambda \mu} \left( q,t \right) \right)_{\lambda, \mu \in \mathcal{P}_d}$ for partitions $\lambda = \mu$ in the set of partitions $\mathcal{P}_d$ of odd positive numbers $d$ with …