Giambelli and degeneracy locus formulas for classical G/P spaces
Let G be a classical complex Lie group, P any parabolic subgroup of G, and X=G/P the corresponding homogeneous space, which parametrizes (isotropic) partial flags of subspaces of a vector space. In the mid 1990s, Fulton and Pragacz asked for global formulas which express the cohomology classes of the universal Schubert varieties in flag bundles -- when the space X varies in an algebraic family -- in terms of the Chern classes of the vector bundles involved in their definition. We will explain our answer to this question, expressed in terms of combinatorial data coming from the Weyl group.