1207.2823 (Xiaoli Hu et al.)

Generalized McKay quivers of rank three    [PDF]

Xiaoli Hu, Naihuan Jing, Wuxing Cai

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.

View original: http://arxiv.org/abs/1207.2823