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<p>In this paper, we first show that the functions associated with specific linear transformations of the vertex operator presentation of the universal character are polynomial tau functions of the UC hierarchy. Subsequently, we explore a generalization of dual stable <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10801_2025_1444_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-Grothendieck polynomials, which serves as an instance of such linear transformation. We then provide their vertex operator and fermion realizations and prove that these functions are polynomial tau functions of the UC hierarchy.</p>

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Grothendieck universal character and polynomial tau functions for UC hierarchy

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • Fang Huang,
  • Chuanzhong Li

摘要

In this paper, we first show that the functions associated with specific linear transformations of the vertex operator presentation of the universal character are polynomial tau functions of the UC hierarchy. Subsequently, we explore a generalization of dual stable \(\beta \) β -Grothendieck polynomials, which serves as an instance of such linear transformation. We then provide their vertex operator and fermion realizations and prove that these functions are polynomial tau functions of the UC hierarchy.