Even orthogonal Grassmannian $OG(m,2n)$ are the spaces parameterize $m$-dimensianl isotropic subspaces in a vector space $V\simeq \mathbb{C}^{2n}$, with a nondegenerate symmetric bilinear form. It's the Grassmannian of type D.
I know that the cohomology ring of $H^*(OG(m,2n),\mathbb{Z})$ can be presented as the quotient of a polynomial ring, with the variables are the cohomolgy class of some special varieties. Are there any good reference for the detail of this ring?
A complete description of the cohomology rings in terms of Schubert calculus is given in the beginning of this paper https://arxiv.org/pdf/math/0306338.pdf. See the bottom of page 1- the top of page 2.