  Consider a pair of symplectic varieties dual with respect to 3D-mirror
symmetry. The K-theoretic limit of the elliptic duality interface is an
equivariant K-theory class of the product. We show that this class provides
correspondences in the product mapping the K-theoretic stable envelopes to the
K-theoretic stable envelopes. This construction allows us to extend the action
of various representation theoretic objects on K(X), such as action of quantum
groups, quantum Weyl groups, R-matrices etc., to their action on the K-theory
of the variety dual to X. In particular, we relate the wall R-matrices to the
R-matrices of the dual variety.
  As an example, we apply our results to the Hilbert scheme of n points in the
complex plane. In this case we arrive at the conjectures of E.Gorsky and
A.Negut.
