In his work on nilpotent lie
groups, A. A. Kirillov introduced the idea of classifying the representations of such
groups by matching them with orbits in the dual of the lie algebra under the
coadjoint action. His methods have proved extremely fruitful, and subsequent authors
have refined and extended them to the point where they provide highly
satisfactory explanations of many aspects of the harmonic analysis of various lie
groups. Meanwhile, it appears that nonlie groups are also amenable to such
an approach. In this paper, we seek to indicate that, indeed, a very large
class of separable, locally compact, nilpotent groups have a Kirillov-type
theory.
