  For each finite subgroup G of SL(n, C), we introduce the generalized Cartan
matrix C_{G} in view of McKay correspondence from the fusion rule of its
natural representation. Using group theory, we show that the generalized Cartan
matrices have similar favorable properties such as positive semi-definiteness
as in the classical case of affine Cartan matrices (the case of SL(2,C)). The
complete McKay quivers for SL(3,C) are explicitly described and classified
based on representation theory.
