Local non-rigidity conjecture for Clifford-Klein forms of nilpotent Lie groups

Let $G$ be a 1-connected nilpotent Lie group, $H \subset G$ a closed subgroup, and $\Gamma \subset G$ a non-trivial discrete subgroup. Let $\mathcal{R}(\Gamma,G,H)$ denote the space of representations associated with Clifford-Klein forms of $G/H$. An element is locally rigid if its corresponding Clifford-Klein form admits no nontrivial sufficiently small deformation. Local non-rigidity conjecture. No elements of $\mathcal{R}(\Gamma,G,H)$ are locally rigid. This conjecture asserts that Clifford-Klein forms in the nilpotent case are never locally rigid when the discrete subgroup is non-trivial; its status is stated in the source as unsolved.