We study the K-theoretic enumerative geometry of cyclic Nakajima quiver varieties, with particular focus on \(\text {Hilb}^{n}([\mathbb {C}^{2}/\mathbb {Z}_{l}])\) , the equivariant Hilbert scheme of points on \(\mathbb {C}^2\) . The direct sum over n of the equivariant K-theories of these varieties is known to be isomorphic to the ring symmetric functions in l colors, with structure sheaves of torus fixed points identified with wreath Macdonald polynomials. Using properties of wreath Macdonald polynomials and the recent identification of the Maulik-Okounkov quantum affine algebra for cyclic quivers with the quantum toroidal algebras of type A, we derive an explicit formula for the generating function of capped vertex functions of \(\text {Hilb}^{n}([\mathbb {C}^{2}/\mathbb {Z}_{l}])\) with descendants given by exterior powers of the 0th tautological bundle. We also sharpen the large framing vanishing results of Okounkov, providing a class of descendants and cyclic quiver varieties for which the capped vertex functions are purely classical. Our results also suggest certain integrality and wall-crossing conjectures for capped vertex functions.
