A GIAMBELLI FORMULA FOR CLASSICAL G/P SPACES

Let G be a classical complex Lie group, P any parabolic subgroup of G, and G/P the corresponding partial flag variety. We prove an explicit combinatorial Giambelli formula which expresses an arbitrary Schubert class in H*(G/P) as a polynomial in certain special Schubert class generators. Our formula extends to one that applies to the torus-equivariant cohomology ring of G/P and to the setting of symplectic and orthogonal degeneracy loci.