Valette's conjecture on rapid decay for cocompact semisimple lattices

Let $G$) be a semisimple Lie group, either real or $p$-adic, and let $\Gamma$ be a cocompact lattice in $G$. Valette's conjecture. The group $\Gamma$ has the Rapid Decay property. This conjecture extends the known examples of groups with the Rapid Decay property to cocompact lattices in arbitrary semisimple Lie groups; it remains open, for example, for lattices in $Sp_4(\mathbb{Q}_p)$ and more generally in the groups covered by the conjecture.