TheIn [[mathematics]], the '''Kirillov orbit theorymethod''' or(also known as the '''Kirillov theory''', '''the method of coadjoint orbits''' and by a few similar names) establishes a correspondence between irreducible [[unitary representation]]s of a [[Lie group]] and its [[coadjoint orbit]]s: orbits of the [[group action|action of the group]] on the dual space of its [[Lie algebra]]. The theory was initially developed by [[Alexandre Kirillov]] for [[nilpotent group]]s and later extended by [[Bertram Kostant]], [[Louis Auslander]], [[Lajos Pukánszky]] and others to the case of [[solvable group]]s. [[Roger Evans Howe|Roger Howe]] found a version of the orbit method that applies to ''p''-adic Lie groups. [[David Vogan]] proposed that the orbit method should serve as a unifying principle in the description of the unitary duals of real reductive Lie groups.
