  In an earlier paper, we considered several restriction problems in the
representation theory of classical groups over local and global fields.
Assuming the Langlands-Vogan parameterization of irreducible representations,
we formulated precise conjectures for the solutions of these restriction
problems. In the local case, our conjectural answer is given in terms of
Langlands parameters and certain natural symplectic root numbers associated to
them. In the global case, the conjectural answer is expressed in terms of the
central critical value or derivative of a global $L$-function. In this paper we
verify several of these conjectures in certain low rank cases, using methods of
base change, theta correspondence, and global arguments.
