Restrictions of some unitary representations of SU(n, 1) to U(n − 1, 1)

AbstractLet G be a connected semisimple real Lie group. Let H be a reductive connected subgroup of G. Let us assume that H contains a compact Cartan subgroup of G. In her thesis, S. Martens (Proc. Nat. Acad. Sci. U.S.A. 72, No. 9, 1925, 3275–3276) proved that a holomorphic square integrable representation of G restricts discretely to H. In this paper we prove that for G = SU(2, 1) and H = U(1, 1) the so-called nonholomorphic discrete series of G restricts continuously to H. We also compute restrictions of nondegenerate limits of discrete series of SU(n, 1) to U(n − 1, 1)