Invariant random subgroups of semidirect products

IAN BIRINGER, LEWIS BOWEN, OMER TAMUZ
2018 Ergodic Theory and Dynamical Systems  
We study invariant random subgroups (IRSs) of semidirect products $G=A\rtimes \unicode[STIX]{x1D6E4}$ . In particular, we characterize all IRSs of parabolic subgroups of $\text{SL}_{d}(\mathbb{R})$ , and show that all ergodic IRSs of $\mathbb{R}^{d}\rtimes \text{SL}_{d}(\mathbb{R})$ are either of the form $\mathbb{R}^{d}\rtimes K$ for some IRS of $\text{SL}_{d}(\mathbb{R})$ , or are induced from IRSs of $\unicode[STIX]{x1D6EC}\rtimes \text{SL}(\unicode[STIX]{x1D6EC})$ , where
more » ... $\unicode[STIX]{x1D6EC}<\mathbb{R}^{d}$ is a lattice.
doi:10.1017/etds.2018.46 fatcat:6wropsbhxrfndidlej3tcf6iry