Invariant random subgroups on certain orbits

Key Points

• This study aims to investigate the existence of invariant random subgroups supported on orbits of the conjugation action of connected Lie groups.
• Analysis of the space of closed subgroups of G using Chabauty topology.
• Examination of conjugation actions on the closed subgroups.
• Demonstrated the existence of invariant random subgroups on various conjugate orbits.
• Described structural relationships between the subgroups in the considered space.