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<p>We consider the Knizhnik–Zamolodchikov equations in Deligne Categories in the context of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\mathfrak {gl}_m,\mathfrak {gl}_{n})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="fraktur">gl</mi> <mi>m</mi> </msub> <mo>,</mo> <msub> <mi mathvariant="fraktur">gl</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((\mathfrak {so}_m,\mathfrak {so}_{2n})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="fraktur">so</mi> <mi>m</mi> </msub> <mo>,</mo> <msub> <mi mathvariant="fraktur">so</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> dualities. We derive integral formulas for the solutions in the first case and compute monodromy in both cases.</p>

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Knizhnik–Zamolodchikov Equations in Deligne Categories

  • 期刊论文

  • 发表日期：

    2026年5月2日

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  • P. Etingof,
  • I. Motorin,
  • A. Varchenko,
  • I. Zhu

摘要

We consider the Knizhnik–Zamolodchikov equations in Deligne Categories in the context of \((\mathfrak {gl}_m,\mathfrak {gl}_{n})\) ( gl m , gl n ) and \((\mathfrak {so}_m,\mathfrak {so}_{2n})\) ( so m , so 2 n ) dualities. We derive integral formulas for the solutions in the first case and compute monodromy in both cases.