The Structure of Parabolic Subgroups
The Structure of Parabolic Subgroups
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抛物型子群的结构
DOI：
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发表时间：
2004
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通讯作者：
Kenneth D. Johnson
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作者：
Kenneth D. Johnson
假设G是一个实连通的简单非紧李群，具有（使用标准符号）Iwasawa分解G = KAN。如果M = Z(A)K，则群B = MAN是G的最小抛物子群。由于A是向量群，N是单连通幂零群，B的拓扑结构由M的结构决定。当G是线性群时，M的结构是已知的。然而，如果G不是线性群，那么关于M的可用信息就很少。我们这里的目的是对任何连通的、单连通的、非线性的单连通群G给出群M的描述。
Suppose G is a real connected simple noncompact Lie group with (using standard notation) Iwasawa decomposition G = KAN . If M = Z(A)K, the group B = MAN is a minimal parabolic subgroup of G. Since A is a vector group and N is a simply connected nilpotent group, the topological structure of B is determined by the structure of M. When G is a linear group the structure of M is well known. However, if G is not a linear group there is very little available information about M. Our purpose here is to give a description of the group M for any connected, simply connected, nonlinear simple group G.