摘要翻译：
设G是作用于仿射簇X上的还原群，X中的X是G-轨道不闭的点，S是满足X的G-轨道闭的且不含X的G-稳定闭子簇。本文研究G.R.G在点x上的Co特征的Kempf最优类Omega_G(x,S）；特别地，我们考虑了这种最优性如何转移到G的子群。假设K是G的一个G完全可约子群，它固定x,且设H=C_G(K)^0。我们的主要结果是x的H-轨道也不闭，H的最优类Omega_H(x,S）仅由Omega_G(x,S）中在H中求值的余项组成。我们将这一结果应用于G通过伴随表示作用于其李代数的情形，得到了一些关于与具有良好特征的幂零元相关的余项的新信息。
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英文标题：
《Optimal Subgroups and Applications to Nilpotent Elements》
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作者：
Michael Bate
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Group Theory        群论
分类描述：Finite groups, topological groups, representation theory, cohomology, classification and structure
有限群、拓扑群、表示论、上同调、分类与结构
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  Let G be a reductive group acting on an affine variety X, let x in X be a point whose G-orbit is not closed, and let S be a G-stable closed subvariety of X which meets the closure of the G-orbit of x but does not contain x. In this paper, we study G.R. Kempf's optimal class Omega_G(x,S) of cocharacters of G attached to the point x; in particular, we consider how this optimality transfers to subgroups of G.   Suppose K is a G-completely reducible subgroup of G which fixes x, and let H = C_G(K)^0. Our main result says that the H-orbit of x is also not closed, and the optimal class Omega_H(x,S) for H simply consists of the cocharacters in Omega_G(x,S) which evaluate in H. We apply this result in the case that G acts on its Lie algebra via the adjoint representation to obtain some new information about cocharacters associated with nilpotent elements in good characteristic.
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PDF链接：
https://arxiv.org/pdf/0708.0477