Kirillov orbit method
Statement
The Kirillov orbit method, sometimes simply called the orbit method when used in a general sense, is a method (or collection of methods) that etablishes a bijection between irreducible representations on the one hand and coadjoint orbits (orbits for the coadjoint representation) on the other hand, for a Lie group of a suitable sort. Under certain circumstances, these sets also come equipped with topologies, and part of what the orbit method shows is that the bijection preserves the topology (i.e., is continuous, or even stronger, is a homeomorphism).
Unlike the observation that number of irreducible representations equals number of conjugacy classes, where there is no explicit bijection, this observation involves building an actual element-to-element bijection between irreducible representations and coadjoint orbits.