Building on work from Sun and Kechris-Quorning, we prove that every acylindrically hyperbolic group 𝐺 admits a weakly mixing probability measure preserving action 𝐺 ↷ (𝑋, , 𝜇) which is faithful but not essentially free. In other words, 𝐺 admits a weakly mixing nontrivial faithful IRS. We also prove that every nonelementary hyperbolic group admits a characteristic random subgroup with the same properties.

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We find a necessary condition for the existence of an action of a Lie group G by quaternionic automorphisms on an integrable quaternionic manifold in terms of representations of g. We check this condition and prove that a Riemannian symmetric space of dimension 4n for n ≥ 2 has an invariant integrable almost quaternionic structure if and only if it is quaternionic vector space, quaternionic hyperbolic space or quaternionic projective space.