An old but still open problem in representation theory is a description of the equivalence classes of irreducible, unitary representations of (real reductive) Lie groups. One way to make progress on this problem is the orbit method,[Ki].

The orbit philosophy is a guiding principle in the representation theory of Lie groups and suggests a relation between irreducible unitary representations and coadjoint orbits. These are the orbits under the action of the Lie group on the dual of its Lie algebra. For nilpotent groups, or more generally solvable groups, it can be used to establish a bijective correspondence between coadjoint orbits and irreducible unitary representations, but already for the semisimple group SL (2, R) this correspondence does not cover the whole unitary dual. One of the main problems is the quantisation of nilpotent coadjoint orbits of semisimple groups, which are expected to correspond to rather small unitary representations.