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<p>We construct a family of extremal loop weight modules for the quantum toroidal algebra <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {U}_{q}(\mathfrak {g}^{\textrm{tor}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">U</mi> <mi>q</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="fraktur">g</mi> </mrow> <mtext>tor</mtext> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of type <i>D</i>. By specializing the quantum parameter <i>q</i>, we obtain a family of finite-dimensional modules of quantum toroidal algebras of type <i>D</i> at roots of unity.</p>

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Extremal Loop Weight Modules of Type D Quantum Toroidal Algebras

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Piao-Juan Hu,
  • Jian-Rong Li,
  • Yan-Feng Luo

摘要

We construct a family of extremal loop weight modules for the quantum toroidal algebra \(\mathcal {U}_{q}(\mathfrak {g}^{\textrm{tor}})\) U q ( g tor ) of type D. By specializing the quantum parameter q, we obtain a family of finite-dimensional modules of quantum toroidal algebras of type D at roots of unity.