  Let V be a 2n-dimensional complex symplectic space. Let G' be the Lagrangian
Grassmannian of maximal isotropic subspaces of V embedded via the inclusion i
into the Grassmannian G of all n-dimensional subspaces of V. We discuss the
restriction via i* of a Schubert class from H(G), as an integral linear
combination of Schubert classes in H(G'). Among the main tools we mention
Stembridge's results on shifted tableaux. Using these results and a
generalization of the Macdonald-You identity from an earlier author's paper, we
establish several related algebro-geometric formulas.
