Biringer, Ian and Bowen, Lewis and Tamuz, Omer (2020) Invariant random subgroups of semidirect products. Ergodic Theory and Dynamical Systems, 40 (2). pp. 353-366. ISSN 0143-3857. doi:10.1017/etds.2018.46. https://resolver.caltech.edu/CaltechAUTHORS:20170712-084843331
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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<R^d is a lattice.
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| 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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| Issue or Number: | 2 | ||||||||||||||
| DOI: | 10.1017/etds.2018.46 | ||||||||||||||
| Record Number: | CaltechAUTHORS:20170712-084843331 | ||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170712-084843331 | ||||||||||||||
| Official Citation: | BIRINGER, I., BOWEN, L., & TAMUZ, O. (2020). Invariant random subgroups of semidirect products. Ergodic Theory and Dynamical Systems, 40(2), 353-366. doi:10.1017/etds.2018.46 | ||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||
| ID Code: | 78991 | ||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||||
| Deposited On: | 12 Jul 2017 17:15 | ||||||||||||||
| Last Modified: | 15 Nov 2021 17:44 |
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