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.
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.