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Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type II. The Two- and Three-Variable Cases

Martin A. Hallnäs (Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori) ; Simon Ruijsenaars
International mathematics research notices (1073-7928). (2017)
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: relativistic Calogero-Moser systems, analytic difference operators, joint eigenfunctions

Denna post skapades 2017-09-11.
CPL Pubid: 251817


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Institutionen för matematiska vetenskaper, Analys och sannolikhetsteoriInstitutionen för matematiska vetenskaper, Analys och sannolikhetsteori (GU)


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