  We study three related topics in representation theory of classical Lie
superalgebras. The first one is classification of primitive ideals, i.e.
annihilator ideals of simple modules, and inclusions between them. The second
topic concerns Arkhipov's twisting functors on the BGG category O. The third
topic addresses deformed orbits of the Weyl group. These take over the role of
the usual Weyl group orbits for Lie algebras, in the study of primitive ideals
and twisting functors for Lie superalgebras.
