Stabilizers for ergodic actions of higher rank semisimple groups (Q1334326)

Let \(G\) be a connected semisimple Lie group with finite center and \(\mathbb{R}\)-rank \(\geq 2\). Suppose that each simple factor of \(G\) either has \(\mathbb{R}\)-rank \(\geq 2\) or is locally isomorphic to \(\text{Sp} (1,n) F_{4 (-20)}\). Then the authors prove that any faithful, irreducible, properly ergodic, finite measure-preserving action of \(G\) is essentially free. They also extend the result to reducible actions and actions of lattices. One of the key ingredients is a result of the second author generalizing a result of Margulis on measurable equivalent quotients of flag varieties.