A Giambelli formula for even orthogonal Grassmannians (Q890760)

Consider a complex vector space \(V\) of dimension \(N\) equipped with a nondegenerate symmetric form. Choose an integer \(m < N/2\) and consider the Grassmannian \(\mathrm{OG}=\mathrm{OG}(m; N)\) parametrizing isotropic \(m\)-dimensional subspaces of \(V\). In this paper the authors prove a Giambelli formula expressing the Schubert classes on OG as polynomials in certain special Schubert classes that generate the cohomology ring \(H^* (\mathrm{OGF};\mathbb Z)\) for the even \(N\).