Generalized McKay quivers of rank three
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- 作者：Xiao Li Hu (11005)
Naihuan Jing (11005) (21005)
Wu Xing Cai (11005) - 关键词：McKay correspondence ; McKay quivers ; generalized Dynkin diagrams ; 20H99 ; 14E16 ; 22E40
- 刊名：Acta Mathematica Sinica
- 出版年：2013
- 出版时间：July 2013
- 年：2013
- 卷：29
- 期：7
- 页码：1351-1368
- 全文大小：353KB
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Naihuan Jing (11005) (21005)
Wu Xing Cai (11005)
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 - ISSN：1439-7617
文摘
For each finite subgroup G of SL n (?, 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 semidefiniteness as in the classical case of affine Cartan matrices. The complete McKay quivers for SL 3(? are explicitly described and classified based on representation theory.