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<p>We consider two new families of quantum vertex algebras which are associated with the type <i>A</i> trigonometric <i>R</i>-matrix and elliptic <i>R</i>-matrix of the eight-vertex model. We show that their <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5402_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>-coordinated representation theory is governed by the so-called FRT-operator, <i>h</i>-adically restricted operator satisfying the FRT-relation, and we demonstrate some applications of this result. Finally, in the elliptic case, we investigate the properties of the quantum determinant associated with the corresponding quantum vertex algebra.</p>

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On Two Families of Quantum Vertex Algebras of FRT-Type

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Lucia Bagnoli,
  • Marijana Butorac,
  • Slaven Kožić

摘要

We consider two new families of quantum vertex algebras which are associated with the type A trigonometric R-matrix and elliptic R-matrix of the eight-vertex model. We show that their \(\phi \) ϕ -coordinated representation theory is governed by the so-called FRT-operator, h-adically restricted operator satisfying the FRT-relation, and we demonstrate some applications of this result. Finally, in the elliptic case, we investigate the properties of the quantum determinant associated with the corresponding quantum vertex algebra.