Invariant random subgroups and action versus representation maximality

Peter J. Burton, Alexander S. Kechris

Published 2016-08-03Version 1

We show that weak containment of free ergodic measure-preserving actions of $\mathbf{F}_\infty$ is not equivalent to weak containment of the corresponding Koopman representations. This result is based on the construction of an invariant random subgroup of $\mathbf{F}_\infty$ which is supported on the maximal actions.