On the invariant theory and geometry of compact linear groups of cohomogeneity⩽3
On the invariant theory and geometry of compact linear groups of cohomogeneity⩽3
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关于同齐性紧线性群⩽3的不变理论和几何
DOI：
10.1016/0926-2245(94)00007-7
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发表时间：
1994
影响因子：
0.5
通讯作者：
E. Straume
中科院分区：
文献类型：
--
作者：
E. Straume
本文研究了齐性≥3的紧线性群，即具有暗淡R n⧸G≤3的正交群O (n)的闭子群G。主要问题是确定不变量环以及S n−1⧸G的轨道距离度量，对于所有同质性3的群。出发点是已知的这种紧连通线性群的分类，基本思想是充分利用通常称为约简原则的技术。虽然主各向同性群及其归一化器的计算可能是相当技术性的，但方法是相当初级的。一些材料是解释性的，因为我们试图呈现完整的结果，也力求在任何可能的地方都是独立的。
The paper is concerned with compact linear groups of cohomogeneity⩽ 3, namely closed subgroups G of the orthogonal group O (n) with dim R n⧸ G⩽ 3. The main issue is to determine the ring of invariants as well as the orbital distance metric of S n− 1⧸ G, for all groups of cohomogeneity 3. The starting point is the known classification of compact connected linear groups of this type, and the basic idea is to fully utilize a technique usually referred to as the reduction principle. Although the calculations of principal isotropy groups and their normalizers can be quite technical, the approach is rather elementary. Some of the material is of an expository nature since we try to present complete results and also strive to be selfcontained wherever possible.