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<p>A non-abelian generalisation of a birational representation of affine Weyl groups and their application to the discrete dynamical systems is presented. By using this generalisation, non-commutative analogs for the discrete systems of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A_n^{(1)}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>A</mi> <mi>n</mi> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n \ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> type and of <i>d</i>-Painlevé equations with an additive dynamic were derived. A coalescence cascade of the later is also discussed.</p>

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Affine Weyl Groups and Non-Abelian Discrete Systems: An Application to the d-Painlevé Equations

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Irina Bobrova

摘要

A non-abelian generalisation of a birational representation of affine Weyl groups and their application to the discrete dynamical systems is presented. By using this generalisation, non-commutative analogs for the discrete systems of \(A_n^{(1)}\) A n ( 1 ) , \(n \ge 2\) n ≥ 2 type and of d-Painlevé equations with an additive dynamic were derived. A coalescence cascade of the later is also discussed.