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Award ID contains: 2401380

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  1. ; (, Letters in Mathematical Physics)
    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. 
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    Free, publicly-accessible full text available June 1, 2026
  2. ; (, Letters in Mathematical Physics)
    Free, publicly-accessible full text available June 1, 2026
  3. ; (, Arnold Mathematical Journal)
    In this note we discuss an integral representation for the vertex function of the cotangent bundle over the Grassmannian, $$X=T^{*}\Gr(k,n)$$. This integral representation can be used to compute the $$\hbar\to \infty$$ limit of the vertex function, where $$\hbar$$ denotes the equivariant parameter of a torus acting on $$X$$ by dilating the cotangent fibers. We show that in this limit the integral turns into the standard mirror integral representation of the $$A$$-series of the Grassmannian $$\Gr(k,n)$$ with the Laurent polynomial Landau-Ginzburg superpotential of Eguchi, Hori and Xiong. 
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