Abstract
Let
be an orthogonal Grassmannian parametrizing isotropic
subspaces in an even dimensional vector space equipped with a
nondegenerate symmetric form. We prove a Giambelli formula which
expresses an arbitrary Schubert class in the classical and quantum
cohomology rings of
as a polynomial in certain special Schubert
classes. Our analysis reveals a surprising relation between the
Schubert calculus on even and odd orthogonal Grassmannians. We also
study
, a family of polynomials defined using
raising operators whose algebra agrees with the Schubert calculus on