Calogero–Sutherland hyperbolic system and Heckman–Opdam gln hypergeometric function

• N. Belousov ^[2] ; L. Cherepanov ^[1] ; S. Derkachov ^[2] ; S. Khoroshkin ^[2]
  1. [1] Higher School of Economics, National Research University

     Higher School of Economics, National Research University

     Rusia

     
  2. [2] Beijing Institute of Mathematical Sciences and Applications, China
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 3, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-026-01148-8
• Enlaces
  • Texto completo
• Resumen

  • 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 gln hypergeometric function.

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