Let the vector bundle 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 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 [6] describes physical aspects of the theory, including a conjecture for the
quantum sheaf cohomology ring, and numerous examples.