In #mathematics, the orbit method (also known as the #Kirillov theory, the method of #coadjointOrbits and by a few similar names) establishes a correspondence between #irreducible #unitaryRepresentations of a #LieGroup and its coadjoint orbits: orbits of the #actionOfTheGroup on the #dualSpace of its #LieAlgebra. The theory was introduced by Kirillov (1961, 1962) for #nilpotentGroups and later extended by #BertramKostant, #LouisAuslander, #LajosPukánszky.