Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups
Journal article, 2016
We consider the spherical complementary series of rank one Lie groups H-n = SO0(n, 1; F) for F = R, C, H. We prove that there exist finitely many discrete components in its restriction under the subgroup Hn-1 = SO0(n - 1, 1; F). This is proved by imbedding the complementary series into analytic continuation of holomorphic discrete series of G(n) = SU (n, 1), SU (n, 1) x SU (n, 1) and SU (2n, 2) and by the branching of holomorphic representations under the corresponding subgroup G(n-1).
spherical principal series