A Giambelli formula for isotropic Grassmannians

Abstract

Let X be a symplectic or odd orthogonal Grassmannian. We prove a Giambelli formula which expresses an arbitrary Schubert class in \({{\mathrm{\mathrm {H}}}}^*(X,{\mathbb Z})\) 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.