Restriction des s\'eries discr\`etes de SU(2,1) \`a un sous-groupe exponentiel maximal et \`a un sous-groupe de Borel

We give an explicit description of the restriction of discrete series representations of SU(2,1) to a Borel subgroup and to a maximal exponential solvable subgroup and we interpret our results in the framework of orbit method, Hamiltonian geometry and "$\text{Spin}_{c}$" quantization. Our results give a positive answer to a Duflo's conjecture for SU(2,1).