Pursuing quantum difference equations II: 3D-mirror symmetry

Understand

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.