  Suppose G is a real reductive Lie group in Harish-Chandra's class. We propose
here a structure for the set \Pi_u(G) of equivalence classes of irreducible
unitary representations of G. (The subscript u will be used throughout to
indicate structures related to unitary representations.) We decompose
\Pi_{u}(G) into disjoint subsets with a (very explicit) discrete parameter set
\Lambda_u: \Pi_u(G) = \bigcup_{\lambda_u \in \Lambda_u} \Pi_u^{\lambda_u}(G).
Each subset is identified conjecturally with a collection of unitary
representations of a certain subgroup G(\lambda_u) of G. (We will give strong
evidence and partial results for this conjecture.) In this way the problem of
classifying \Pi_u(G) would be reduced (by induction on the dimension of G) to
the case G(\lambda_u) = G.
