  We consider several questions about restriction of representations of
classical and metaplectic groups over local and global fields to subgroups,
extending considerably the scope of the earlier work on $SO(n),SO(n-1)$. This
includes Bessel and Fourier-Jacobi models too. We formulate several conjectures
about these restriction problems involving root numbers of symplectic
representations in the local case, and central critical L-value in the global
case. Along the way we prove several results both in number theory and
representation theory.
