Stabilizer rigidity in irreducible group actions

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• 作者：Yair Hartman ; Omer Tamuz
• 刊名：Israel Journal of Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：216
• 期：2
• 页码：679-705
• 全文大小：306 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Group Theory and Generalizations
  Analysis
  Applications of Mathematics
  Mathematical and Computational Physics
  
• 出版者：Hebrew University Magnes Press
• ISSN：1565-8511
• 卷排序：216

文摘

We consider irreducible actions of locally compact product groups, and of higher rank semi-simple Lie groups. Using the intermediate factor theorems of Bader–Shalom and Nevo–Zimmer, we show that the action stabilizers, and all irreducible invariant random subgroups, are co-amenable in their normal closure. As a consequence, we derive rigidity results on irreducible actions that generalize and strengthen the results of Bader–Shalom and Stuck–Zimmer.