  Generalizations of the AGT correspondence between 4D $\mathcal{N}=2$ $SU(2)$
supersymmetric gauge theory on ${\mathbb {C}}^2$ with $\Omega$-deformation and
2D Liouville conformal field theory include a correspondence between 4D
$\mathcal{N}=2$ $SU(N)$ supersymmetric gauge theories, $N = 2, 3, \ldots$, on
${\mathbb {C}}^2/{\mathbb {Z}}_n$, $n = 2, 3, \ldots$, with
$\Omega$-deformation and 2D conformal field theories with $\mathcal{W}^{\,
para}_{N, n}$ ($n$-th parafermion $\mathcal{W}_N$) symmetry and
$\widehat{\mathfrak{sl}}(n)_N$ symmetry. In this work, we trivialize the factor
with $\mathcal{W}^{\, para}_{N, n}$ symmetry in the 4D $SU(N)$ instanton
partition functions on ${\mathbb {C}}^2/{\mathbb {Z}}_n$ (by using specific
choices of parameters and imposing specific conditions on the $N$-tuples of
Young diagrams that label the states), and extract the 2D
$\widehat{\mathfrak{sl}}(n)_N$ WZW conformal blocks, $n = 2, 3, \ldots$, $N =
1, 2, \ldots\, .$
