Calogero-Sutherland hyperbolic system and Heckman-Opdam $\mathfrak{gl}_n$ hypergeometric function
Mathematical Physics
2026-01-21 v3 Classical Analysis and ODEs
math.MP
Representation Theory
Exactly Solvable and Integrable Systems
Abstract
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 hypergeometric function.
Keywords
Cite
@article{arxiv.2508.18864,
title = {Calogero-Sutherland hyperbolic system and Heckman-Opdam $\mathfrak{gl}_n$ hypergeometric function},
author = {N. Belousov and L. Cherepanov and S. Derkachov and S. Khoroshkin},
journal= {arXiv preprint arXiv:2508.18864},
year = {2026}
}