UNIVERSAL GRAPH SCHUBERT VARIETIES

We consider the loci of invertible linear maps f : ℂn → (ℂn)* together with pairs flags (E•, F•) in such that various restrictions Fj $$ {E}_i^{\ast } have specified ranks. Identifying an map its graph viewed as a point Grassmannian, we show closures these cohomology classes represented by back-stable Schubert polynomials Lam, Lee, and Shimozono. As special case, recover result Knutson, Speyer Stanley symmetric functions represent varieties. similar where is restricted to be or skew-symmetric. Their are now given versions introduced Wyser Yong orbit for orthogonal symplectic groups acting on type A flag variety. Using degeneracy locus formulas Kazarian Anderson Fulton, obtain new Pfaffian vexillary case. also give geometric interpretation involution Hamaker, Marberg, author: they varieties isotropic Grassmannians.