Capped vertex functions for \({\text {Hilb}}^n(\mathbb {C}^2)\)

We obtain explicit formulas for the K-theoretic capped descendent vertex functions of \({\text {Hilb}}^n(\mathbb {C}^2)\) for descendents given by the exterior algebra of the tautological bundle. This formula provides a one-parametric deformation of the generating function for normalized Macdonald polynomials. In particular, we show that the capped vertex functions are rational functions of the quantum parameter.