Integral and higher-genus quantum McKay correspondence in type D

We establish Iritani's integral form of the $\mathbb{C}^\times$-equivariant Crepant Transformation Conjecture (CTC) for the minimal resolution of the surface singularity $\mathbb{C}^2/\mathbb{BD}_{4n}$, where $\mathbb{BD}_{4n}$ is the binary dihedral group of order $4n$. We then use Givental's quant