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In this paper, we explore a consequence of symplectic duality (also known as3d mirror symmetry) in the setting of enumerative geometry. The theory ofquasimaps allows one to associate hypergeometric functions called vertexfunctions to quiver varieties. In this paper, we prove a formula which relatesthe vertex functions of $T^*Gr(k,n)$ and its symplectic dual. In the course ofthe proof, we study a family of $q$-difference operators which act diagonallyon Macdonald polynomials. Our results may be interpreted from a combinatorialperspective as providing an evaluation formula for a $q$-Selberg type integral.

Symplectic Duality of $T^*Gr(k,n)$