  Suppose $G$ is a real reductive group. The determination of the irreducible
unitary representations of $G$ is one of the major unsolved problem in
representation theory. There is evidence to suggest that every irreducible
unitary representation of $G$ can be constructed through a sequence of
well-understood operations from a finite set of building blocks, called the
unipotent representations. These representations are `attached' (in a certain
mysterious sense) to the nilpotent orbits of $G$ on the dual space of its Lie
algebra. Inside this finite set is a still smaller set, consisting of the
unipotent representations attached to non-induced nilpotent orbits. In this
paper, we prove that in many cases this smaller set generates (through a
suitable kind of induction) all unipotent representations.
