  This paper is the fourth and last in the series "On the classification of
primitive ideals for complex classical Lie algebras", extending earlier results
in other classical types to type D. The generalized tau-invariant used in
earlier work must now be defined in a different way, using a family of
operators attached to a quadruple of simple roots spanning a subsystem of type
D_4. each taking one or two values. Using these operators we show that
primitive ideals of trivial infinitesimal character are characterized by their
generalized tau-invariants and are parametrized by standard domino tableaux of
the appropriate special shape.
