A new relation among Cartan matrix and Coxeter matrix
A new relation among Cartan matrix and Coxeter matrix
复制标题
Cartan矩阵与Coxeter矩阵之间的新关系
DOI：
10.1016/0021-8693(87)90183-9
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发表时间：
1987
影响因子：
0.9
通讯作者：
Kyoji Saito
中科院分区：
文献类型：
--
作者：
Kyoji Saito
这里pqrfd是关于第1节中定义的R的Cartan矩阵的数值不变量，u/x/h是关于第2节中定义的R的Coxeter iransformatioI 1的数值不变量。利用有理曲面上Weil因子的自交数证明了第四节中的等式。这个论点是一个版本的奇怪的对偶性的14个特殊的幺模奇点阿诺德由于平卡姆（cf。[1，61]。找到一个纯粹的算术证明这个等式可能是很有趣的。作者想向我的同事们表达他的敬意。Naruki和M.感谢托马里的关心和有益的讨论，也感谢K。上野，谁注意到作者的一些作品反典型因子。
Here pqrfd is a numerical invariant concerning about the Cartan matrix of R defined in Section 1 and u/x/h is a numerical invariant concerning about a Coxeter iransformatioI1 of R defined in Section 2. We give a proof of the equality in Section 4 using the self-intersection number of a Weil divisor on a rational surface. The argument is a version of that for the strange duality on the 14 exceptional unimodular singularities of Arnold due to Pinkham (cf.[1, 61). It might be quite interesting to find a purely arithmetic proof of the equality. The author would like to express his glatitude to his colleages I. Naruki and M. Tomari for their interest and helpful1 discussions and also to K. Ueno, who has noticed the author on some works on anti-canonical divisors.