  We give a conjectural formula for sheaves supported on (irreducible) conormal
varieties inside the cotangent bundle of the Grassmannian, such that their
equivariant $K$-class is given by the partition function of an integrable loop
model, and furthermore their $K$-theoretic pushforward to a point is a solution
of the level $1$ quantum Knizhnik-Zamolodchikov equation. We prove these
results in the case that the Lagrangian is smooth (hence is the conormal bundle
to a subGrassmannian). To compute the pushforward to a point, or equivalently
to the affinization, we simultaneously degenerate the Lagrangian and sheaf
(over the affinization); the sheaf degenerates to a direct sum of cyclic
modules over the geometric components, which are in bijection with plane
partitions, giving a geometric interpretation to the Razumov-Stroganov
correspondence satisfied by the loop model.
