Abstract: The McKay correspondence is a beautiful connection between finite groups and algebraic geometry. For instance, the geometry properties of the resolved $C^n/\Gamma$ orbifold singularity shall be read out from the group theoretic data of $\Gamma$, a finite subgroup of SU(n). Physically, we consider superstring/M-theory engineered on the $C^n/\Gamma$ singularity, resulting in lower-dimensional supersymmetric field theories. I will present the basic example of n=2, our previous works on the n=3 case, and an upcoming work on the n=4 case. We find that the McKay quiver data have very nice relations to the generalized global symmetries of the lower-dimensional supersymmetric field theories.