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The method of coadjoint orbits suggests that irreducible unitary r epresentations of a Lie group $G$ are something like quantum mechanical systems. In fact finding all irreducible unitary representation of nilpotent lie groups correspounds to geometric quantization of coadjoint orbits. In fact quantiz ation problem comes down to a finite set of coadjoint orbits for each reductive group: the nilpotent orbits.