McKay correspondence and equivariant sheaves on $\mathbb P^1$

Let $G$ be a finite subgroup in ${\rm SU}(2)$, and $Q$ the corresponding affine Dynkin diagram. In this paper, we review the relation between the categories of $G$-equivariant sheaves on $\mathbb P^1$ and Rep $Q_h$, where $h$ is an orientation of $Q$, constructing an explicit equivalence of corresponding derived categories.