The strong quantization conjecture for Lie normalizers

Let ${\mathfrak b}$ be a finite-dimensional basic algebra, and let ${\mathfrak n}({\mathfrak b})$ be its Lie normalizer in $P({\mathfrak b})$. Strong quantization conjecture. Every quantization of ${\mathfrak b}$ can be extended to a quantization of $({\mathfrak n}({\mathfrak b}),{\mathfrak b})$. This conjecture asks whether a representation of the basic algebra always extends to its Lie normalizer, an infinitesimal analogue of a Mackey system of imprimitivity. The source gives no resolution; quantizations satisfying this extension property are called strong by GGT.