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<p>We introduce and study Lyndon bases of the split <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\imath \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ı</mi> </math></EquationSource> </InlineEquation>quantum groups <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\textbf{U}^\imath (\mathfrak {g})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi mathvariant="bold">U</mi> <mi>ı</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Especially, we provide the relation between Lyndon bases and Lusztig’s PBW-type bases of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\textbf{U}^\imath (\mathfrak {g})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi mathvariant="bold">U</mi> <mi>ı</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, as well as a construction of canonical bases of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\textbf{U}^\imath (\mathfrak {g})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi mathvariant="bold">U</mi> <mi>ı</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> under an integral condition.</p>

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Lyndon bases of split \(\imath \)quantum groups

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Run-Qiang Jian,
  • Li Luo,
  • Xianfa Wu

摘要

We introduce and study Lyndon bases of the split \(\imath \) ı quantum groups \(\textbf{U}^\imath (\mathfrak {g})\) U ı ( g ) . Especially, we provide the relation between Lyndon bases and Lusztig’s PBW-type bases of \(\textbf{U}^\imath (\mathfrak {g})\) U ı ( g ) , as well as a construction of canonical bases of \(\textbf{U}^\imath (\mathfrak {g})\) U ı ( g ) under an integral condition.