A Giambelli formula for isotropic Grassmannians

Let X be a symplectic or odd orthogonal Grassmannian. We prove a Giambelli formula which expresses an arbitrary Schubert class in H^*(X,ℤ) as a polynomial in certain special Schubert classes. This polynomial, which we call a theta polynomial , is defined using raising operators, and we study its image in the ring of Billey–Haiman Schubert polynomials.