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<p>We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also the value at zero point, we identify them with renormalized Heckman–Opdam&#xa0;<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathfrak {gl}_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="fraktur">gl</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> hypergeometric function.</p>

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Calogero–Sutherland hyperbolic system and Heckman–Opdam \(\mathfrak {gl}_n\) hypergeometric function

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • N. Belousov,
  • L. Cherepanov,
  • S. Derkachov,
  • S. Khoroshkin

摘要

We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also the value at zero point, we identify them with renormalized Heckman–Opdam  \(\mathfrak {gl}_n\) gl n hypergeometric function.