Plancherel theorem for the affine symmetric space SU(1,2)/SO(1,2)
The irreducible decomposition of unitary representations is investigated on the Hilbert space L2(Z,μ),where Z = SU(1,2)/SO(1,2),and μ denotes an SU(1,2)-invariant Haar measure on Z.By using the SO(1,2)-invariant distribution functions,the intertwining operators is constructed concrete-ly,and then the discrete series representations on L2(Z,μ)are obtained.On this basis,combined with the orthogonal complement parts of the discrete series representations,the Plancherel formula on L2(Z,μ)is proved.
国家科技期刊平台
NSTL
万方数据
维普
