Dimension Formula for Slice for Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras
Dimension Formula for Slice for Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras
复制标题
复简单李代数球面幂零轨道可见作用切片的维数公式
DOI：
10.1007/978-3-319-65181-1_8
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Sasaki Atsumu
中科院分区：
文献类型：
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作者：
Baba Kurando;Ikawa Osamu;Sasaki Atsumu;Sasaki Atsumu
最近的文献[19]从T.小林。本文的目的是给出球面幂零轨道上强可见作用的切片的维数公式。这为球面幂零轨道上作用的强可见性提供了一个统一的解释。进一步，我们证明了我们对这个作用的切片的选择满足它的维数等于幂零轨道的秩，这表明了复几何与复幂零轨道中的多重性自由表示之间的深刻关系.
The recent paper [19] has studied spherical nilpotent orbits in complex simple Lie algebras from the viewpoint of the notion of strongly visible actions introduced by T. Kobayashi. The aim of this paper is to give a dimension formula for a slice for the strongly visible action on a spherical nilpotent orbit. This provides an unified explanation of the strong visibility for the action on a spherical nilpotent orbit. Further, we prove that our choice of slice for this action satisfies its dimension equals the rank of a nilpotent orbit, which suggests a deep relation between complex geometry and multiplicity-free representation in complex nilpotent orbits.