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<p>We consider the Riemann–Hilbert correspondence associated with the <i>q</i>-difference sixth Painlevé equation in the crystal limit, i.e., <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="332_2024_10124_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(q\rightarrow 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, and show two main results. First, the limit of this generically highly transcendental mapping is shown to exist. Second, we show that the limiting map is bi-rational and describe it explicitly.</p>

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On the Crystal Limit of the q-Difference Sixth Painlevé Equation

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  • 发表日期：

    2025年1月9日

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  • Nalini Joshi,
  • Pieter Roffelsen

摘要

We consider the Riemann–Hilbert correspondence associated with the q-difference sixth Painlevé equation in the crystal limit, i.e., \(q\rightarrow 0\) q → 0 , and show two main results. First, the limit of this generically highly transcendental mapping is shown to exist. Second, we show that the limiting map is bi-rational and describe it explicitly.