On matrices in prescribed conjugacy classes with no common invariant subspace and sum zero
On matrices in prescribed conjugacy classes with no common invariant subspace and sum zero
复制标题
关于没有公共不变子空间且和为零的规定共轭类中的矩阵
DOI：
10.1215/s0012-7094-03-11825-6
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发表时间：
2001
影响因子：
2.5
通讯作者：
W. Crawley
中科院分区：
文献类型：
--
作者：
W. Crawley
我们确定这些$k$-元组的共轭类的矩阵，从它可以选择矩阵，没有共同的不变子空间，并有总和为零。这是Deligne-Simpson问题的一个附加版本。我们推导出的结果，从早期的工作，我们的预投射代数和时刻地图表示的箭图。我们的答案取决于Kac-Moody李代数的根系。
We determine those $k$-tuples of conjugacy classes of matrices from which it is possible to choose matrices that have no common invariant subspace and have sum zero. This is an additive version of the Deligne-Simpson problem. We deduce the result from earlier work of ours on preprojective algebras and the moment map for representations of quivers. Our answer depends on the root system for a Kac-Moody Lie algebra.