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.

25 pages

References in corpus (2)

• Kesten's theorem for Invariant Random Subgroups
• Furstenberg entropy realizations for virtually free groups and lamplighter groups

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