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Capped Vertex Functions for $\text{Hilb}^n (\mathbb{C}^2)$
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abstract
We obtain explicit formulas for 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.
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Cited by 1 Pith paper
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Rationality of the K-theoretical capped vertex function for Nakajima quiver varieties
For any Nakajima quiver variety with generic stability condition, the capped vertex function with descendents is a rational function of the Kähler variables.
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