Invariant random subgroups on certain orbits

Abstract

Let $G$ be a connected Lie group and ${\text{Sub}}_G$ be the space of closed subgroups of $G$ equipped with the Chabauty topology. In this article, we investigate the existence of invariant random subgroups of $G$ supported on various orbits of the conjugation action of $G$ on ${\text{Sub}}_G$.

The previous version of the article with the title "IRS on orbits and the case of $\SL(2,\mathbb{R})\ltimes \mathbb{R}^2$" is now made into two separate articles. The first one is the present one with the title "Invariant random subgroups on certain orbits". The second one will appear soon on the arXiv with a different title