Dynkin曲线的轨道结构
The orbit structure of Dynkin curves
摘要：
设G是一个代数闭域k上的单代数群，假设Char k对G为零或良.设\cB是G的博雷尔子群的簇，e在Lie G中是幂零的.存在G中e的中心化子C_G（e）对Springer纤维\cB_e = {B' in \cB| e在Lie B '}中与e关联。在本文中，我们考虑的情况下，其中e位于次正则幂零轨道，在这种情况下，\cB_e是Dynkin曲线。我们给出了\cB_e中C_G（e）-轨道的完整描述.特别地，我们对C_G（e）作用于\cB_e上的具有多个轨道的不可约分支进行了分类.在一个应用中，我们得到了G的固定博雷尔子群B的所有允许有限个B-轨道的次正则轨道簇的分类。
英文摘要：
Let G be a simple algebraic group over an algebraically closed field k; assume that Char k is zero or good for G. Let \cB be the variety of Borel subgroups of G and let e in Lie G be nilpotent. There is a natural action of the centralizer C_G(e) of e in G on the Springer fibre \cB_e = {B' in \cB | e in Lie B'} associated to e. In this paper we consider the case, where e lies in the subregular nilpotent orbit; in this case \cB_e is a Dynkin curve. We give a complete description of the C_G(e)-orbits in \cB_e. In particular, we classify the irreducible components of \cB_e on which C_G(e) acts with finitely many orbits. In an application we obtain a classification of all subregular orbital varieties admitting a finite number of B-orbits for B a fixed Borel subgroup of G.
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