Multiplicity one theorem in the orbit method

In memory of Professor F. Karpelevic Abstract. Let G ⊃ H be Lie groups, g ⊃ h their Lie algebras, and pr : g ∗ → h ∗ the natural projection. For coadjoint orbits O G ⊂ g ∗ and O H ⊂ h ∗ , we denote by n(O G , O H ) the number of H-orbits in the intersection O G ∩ pr −1 (O H ), which is known as the Corwin-Greenleaf multiplicity function. In the spirit of the orbit method due to Kirillov and Kostant, one expects that n(O G , O H ) coincides with the multiplicity of τ ∈ H occurring in an irreducible unitary representation π of G when restricted to H ,i fπ is 'attached' to O G and τ is 'attached' to O H. Results in this direction have been established for