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<p>We obtain explicit formulas for the <i>K</i>-theoretic capped descendent vertex functions of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11005_2025_1933_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\({\text {Hilb}}^n(\mathbb {C}^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="normal">Hilb</mi> </mrow> <mi>n</mi> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年5月6日

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  • Jeffrey Ayers,
  • Andrey Smirnov

摘要

We obtain explicit formulas for the K-theoretic capped descendent vertex functions of \({\text {Hilb}}^n(\mathbb {C}^2)\) Hilb n ( 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.