Invariant random subgroups of semidirect products

Abstract

We study invariant random subgroups (IRSs) of semidirect products $G=A⋊\Gamma$. In particular, we characterize all IRSs of parabolic subgroups of ${\mathrm{SL}}_d(\mathbb{R})$, and show that all ergodic IRSs of ${\mathbb{R}}^d⋊{\mathrm{SL}}_d(\mathbb{R})$ are either of the form ${\mathbb{R}}^d⋊K$ for some IRS of ${\mathrm{SL}}_d(\mathbb{R})$, or are induced from IRSs of $\Lambda ⋊\mathrm{SL}(\Lambda )$, where $\Lambda <{\mathbb{R}}^d$ is a lattice.

16 pages

References in corpus (1)

• Unimodularity of Invariant Random Subgroups