E. Vasserot described an action of the affine Schur algebra on the equivariant $K$-theory of the cotangent vector bundle to the partial flag variety. The quantum parameter $q$ in this construction corresponds to the complex torus acting by stretching the fibers of the cotangent bundle. The goal of our project is to construct a $q=0$ degeneration of this action. We construct families of operators $E_{i,j}(p)$, $F_{i,j}(p)$, $H_{i,j}(p)$ acting on the equivariant $K$-theory of the partial flag variety and prove that they satisfy certain relations.

This is a joint work in progress with Sergey Arkhipov.