CaltechAUTHORS
  A Caltech Library Service

Invariant random subgroups of semidirect products

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. https://resolver.caltech.edu/CaltechAUTHORS:20170712-084843331

[img] PDF - Submitted Version
See Usage Policy.

187Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20170712-084843331

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/etds.2018.46DOIArticle
https://arxiv.org/abs/1703.01282arXivDiscussion Paper
ORCID:
AuthorORCID
Tamuz, Omer0000-0002-0111-0418
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).
Funders:
Funding AgencyGrant Number
NSFDMS-1611851
NSFDMS-1654114
NSFDMS-0968762
NSFDMS-0954606
Binational Science Foundation (USA-Israel)2008274
Simons Foundation419427
Issue or Number:2
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:23 Jan 2020 17:29

Repository Staff Only: item control page