Invariant random subgroups of semidirect products

Creators: Biringer, Ian; Bowen, Lewis; Tamuz, Omer

Abstract

We study invariant random subgroups (IRSs) of semidirect products G=A⋊Γ. In particular, we characterize all IRSs of parabolic subgroups of SL_d(R), and show that all ergodic IRSs of R^d⋊SL_d(R) are either of the form R^d⋊K for some IRS of SL_d(R), or are induced from IRSs of Λ⋊SL(Λ), where Λ

Additional Information

© 2018 Cambridge University Press. Received 4 March 2017 and accepted in revised form 17 May 2018. We thank the referee for a careful reading of the paper, a number of useful comments, and the suggestion to combine our work with [4] to give a proof of the Nevo–Stuck–Zimmer theorem for SL_n(Z), as described in Remark 1 above. The first author was supported in part by NSF grant DMS-1611851 and CAREER Award DMS-1654114. The second author was supported in part by NSF grant DMS-0968762, NSF CAREER Award DMS-0954606 and BSF grant 2008274. The third author's work was supported by a grant from the Simons Foundation (#419427, Omer Tamuz).

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