Generalized McKay quivers of rank three |
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| Authors: | Xiao Li Hu Naihuan Jing Wu Xing Cai |
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| Affiliation: | 11005. School of Sciences, South China University of Technology, Guangzhou, 510640, P. R. China
21005. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA
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| Abstract: | For each finite subgroup G of SLn (C), we introduce the generalized Cartan matrix A 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 complete McKay quivers for SL3 (C) are explicitly described and classified based on representation theory. |
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| Keywords: | McKay correspondence McKay quivers generalized Dynkin diagrams |
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