Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type II. The Two- and Three-Variable Cases
Artikel i vetenskaplig tidskrift, 2017

In a previous paper we introduced and developed a recursive construction of joint eigenfunctions $J_N(a_+,a_-,b;x,y)$ for the Hamiltonians of the hyperbolic relativistic Calogero-Moser system with arbitrary particle number $N$. In this paper we focus on the cases $N=2$ and $N=3$, and establish a number of conjectured features of the corresponding joint eigenfunctions. More specifically, choosing $a_+,a_-$ positive, we prove that $J_2(b;x,y)$ and $J_3(b;x,y)$ extend to globally meromorphic functions that satisfy various invariance properties as well as a duality relation. We also obtain detailed information on the asymptotic behavior of similarity transformed functions $\rE_2(b;x,y)$ and $\rE_3(b;x,y)$. In particular, we determine the dominant asymptotics for $y_1-y_2\to\infty$ and $y_1-y_2,y_2-y_3\to\infty$, resp., from which the conjectured factorized scattering can be read off.

relativistic Calogero-Moser systems

analytic difference operators

joint eigenfunctions


Martin Hallnäs

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Simon Ruijsenaars

International Mathematics Research Notices

1073-7928 (ISSN) 1687-0247 (eISSN)


Annan matematik

Matematisk analys