Bekka–Valette conjecture on representations of lattices

Let $G$ be a non-compact semisimple Lie group, and let $\Gamma$ be a lattice. A unitary representation of $\Gamma$ is weakly contained in a unitary representation of $G$ restricted to $\Gamma$ if it is weakly contained in that restricted representation.

Bekka–Valette conjecture. There exist unitary representations of $\Gamma$ that are not weakly contained in any representation restricted from $G$.

This conjecture concerns the range of the restriction map from representations of a semisimple Lie group to a lattice. The paper states that it gives an affirmative solution, so the conjecture is solved.