  In this paper, we explore a consequence of symplectic duality (also known as
3d mirror symmetry) in the setting of enumerative geometry. The theory of
quasimaps allows one to associate hypergeometric functions called vertex
functions to quiver varieties. In this paper, we prove a formula which relates
the vertex functions of $T^*Gr(k,n)$ and its symplectic dual. In the course of
the proof, we study a family of $q$-difference operators which act diagonally
on Macdonald polynomials. Our results may be interpreted from a combinatorial
perspective as providing an evaluation formula for a $q$-Selberg type integral.
