Homogenous projective factors for actions of semi-simple Lie groups
Homogenous projective factors for actions of semi-simple Lie groups
复制标题
半单李群作用的齐次投影因子
DOI：
10.1007/s002220050377
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发表时间：
1999
影响因子：
3.1
通讯作者：
R. Zimmer
中科院分区：
文献类型：
--
作者：
A. Nevo;R. Zimmer
摘要：我们利用定常测度的存在性作为基本工具，分析了紧致度量（或Borel）空间X上具有有限中心和真实的秩至少为2的连通半单李群G的连续（或Borel）作用的结构.主要结果有如下推论：设P是G的极小抛物子群，K是极大紧子群。设λ是X上的P-不变概率测度，并假设（X，λ）上的P-作用是混合的。则要么λ在G下不变，要么存在一个真抛物子群Q <$G，和一个可测G-等变因子映射<$：（X，ν）→（G/Q，m），其中ν=<$Kkλdk，m是G/Q上的K-不变测度。此外，该扩张具有相对G不变测度，即（X，ν）是由Q的一个（混合）概率测度保持作用导出的.
Abstract.We analyze the structure of a continuous (or Borel) action of a connected semi-simple Lie group G with finite center and real rank at least 2 on a compact metric (or Borel) space X, using the existence of a stationary measure as the basic tool. The main result has the following corollary: Let P be a minimal parabolic subgroup of G, and K a maximal compact subgroup. Let λ be a P-invariant probability measure on X, and assume the P-action on (X,λ) is mixing. Then either λ is invariant under G, or there exists a proper parabolic subgroup Q⊂G, and a measurable G-equivariant factor map ϕ:(X,ν)→(G/Q,m), where ν=∫Kkλdk and m is the K-invariant measure on G/Q. Furthermore, The extension has relatively G-invariant measure, namely (X,ν) is induced from a (mixing) probability measure preserving action of Q.