Stabilizer rigidity in irreducible group actions

Yair Hartman; Omer Tamuz

doi:10.1007/s11856-016-1424-4

Stabilizer rigidity in irreducible group actions

Yair Hartman^*, Omer Tamuz

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	679-705
Number of pages	27
Journal	Israel Journal of Mathematics
Volume	216
Issue number	2
DOIs	https://doi.org/10.1007/s11856-016-1424-4
State	Published - Oct 1 2016

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s11856-016-1424-4

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title = "Stabilizer rigidity in irreducible group actions",

abstract = "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.",

author = "Yair Hartman and Omer Tamuz",

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AU - Tamuz, Omer

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N2 - 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.

AB - 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.

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Stabilizer rigidity in irreducible group actions

Abstract

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