  Let the vector bundle $\mathcal{E}$ be a deformation of the tangent bundle
over the Grassmannian $G(k,n)$. We compute the ring structure of sheaf
cohomology valued in exterior powers of $\mathcal{E}$, also known as the
polymology. This is the first part of a project studying the quantum sheaf
cohomology of Grassmannians with deformations of the tangent bundle, a
generalization of ordinary quantum cohomology rings of Grassmannians. A
companion physics paper [arXiv:1512.08586] describes physical aspects of the
theory, including a conjecture for the quantum sheaf cohomology ring, and
numerous examples.
