  We describe isotropic orbits for the restricted action of a subgroup of a Lie
group acting on a symplectic manifold by Hamiltonian symplectomorphisms and
admitting an Ad*-equivariant moment map. We obtain examples of Lagrangian
orbits of complex flag manifolds, of cotangent bundles of orthogonal Lie
groups, and of products of flags. We introduce the notion of infinitesimally
tight and study the intersection theory of such Lagrangian orbits, giving many
examples.
