摘要
We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.
We consider the tensor product π_α ？ π_βof complementary series representations π_α and π_β of classical rank one groups SO_0（n, 1）, SU（n, 1） and Sp（n, 1）. We prove that there is a discrete component π_（α＋β）for small parameters α and β（in our parametrization）. We prove further that for SO_0（n, 1） there are finitely many complementary series of the form π_（α＋β＋2j,）j = 0, 1,..., k, appearing in the tensor product π_α ？ π_βof two complementary series π_α and π_β, where k = k（α, β, n） depends on α, β and n.
基金
supported by the Swedish Science Council (VR)
