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 ${\mathbb{C}}^2\mathrm{/}{\mathbb{B}\mathbb{D}}_{4n}$, where ${\mathbb{B}\mathbb{D}}_{4n}$ is the binary dihedral group of order $4n$. We then use Givental’s quantisation formalism to prove the all-genus full-descendent CTC in that case. As an application, we deduce the Bryan-Cadman-Young degree-zero form of the orbifold Gromov-Witten/Donaldson-Thomas correspondence for the Calabi-Yau 3-orbifold $[{\mathbb{C}}^2\mathrm{/}{\mathbb{B}\mathbb{D}}_{4n}]\times \mathbb{C}$.