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arXiv · 1207.2823

Generalized McKay quivers of rank three

Xiaoli Hu·Naihuan Jing·Wuxing Cai
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Abstract

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.

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BibTeXRIS

Xiaoli Hu, Naihuan Jing, Wuxing Cai. 2012-07-12. Generalized McKay quivers of rank three. https://doi.org/10.1007/s10114-013-1005-y

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