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

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