  Let X be a symplectic or odd orthogonal Grassmannian parametrizing isotropic
subspaces in a vector space equipped with a nondegenerate (skew) symmetric
form. We prove a Giambelli formula which expresses an arbitrary Schubert class
in H^*(X,Z) as a polynomial in certain special Schubert classes. We study theta
polynomials, a family of polynomials defined using raising operators whose
algebra agrees with the Schubert calculus on X. Furthermore, we prove that
theta polynomials are special cases of Billey-Haiman Schubert polynomials and
use this connection to express the former as positive linear combinations of
products of Schur Q-functions and S-polynomials.
