Restriction des séries discrètes de SU(2,1) à un sous-groupe exponentiel maximal et à un sous-groupe de Borel

Abstract

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).

This is a presentation of my thesis defended last year