The complete-primality conjecture for primitive ideals of Witt and Virasoro enveloping algebras

Let $\g$ be one of $\W{-1}$, $W$, or $\Vir$, and let $\Ua(\g)$ be its enveloping algebra. Complete-primality conjecture. Every primitive ideal of $\Ua(\g)$ is completely prime. The source presents this as a consequence that would follow if the strong Dixmier-map surjectivity conjecture were true; its resolution would give strong information about the quotient algebras defined by primitive ideals.