Kirillov's Orbit Method, due to the work of Konstant, Auslander and Pukansky, works for solvable Lie groups. Is it possible, using this philosophy/method, to identify the finite dimensional unitary representations of a solvable Lie group in terms of properties of the associated coadjoint orbits?
(Sorry for the crudeness of this question. I'm trying to evaluate whether or not to go down a rabbit hole, and the answer to this question will help me decide!)