On orbit spaces of representations of compact Lie groups
On orbit spaces of representations of compact Lie groups
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DOI：
10.1515/crelle-2012-0084
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发表时间：
2011-09
期刊：
影响因子：
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通讯作者：
Claudio Gorodski;A. Lytchak
中科院分区：
文献类型：
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作者：
Claudio Gorodski;A. Lytchak
我们从商空间（被视为度量空间）的角度研究紧李群的正交表示。我们研究度量空间，它同时是不同表示的商，并研究相应表示的属性。我们获得了一些结构结果并将其应用于研究小共极性的不可约表示。作为一个重要的工具，我们对具有四或五同质性的连通群的所有不可约表示进行分类。
We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and investigate properties of the corresponding representations. We obtain some structural results and apply them to study irreducible representations of small copolarity. As an important tool, we classify all irreducible representations of connected groups with cohomogeneity four or five.