The Elliptic Painlev\'e Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
Mathematical Physics
2020-07-09 v2 math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
The 8-parameter elliptic Sakai difference Painlev\'e equation admits a Lax formulation. We show that a suitable specialization of the Lax equation gives rise to the time-independent Schr\"odinger equation for the 8-parameter 'relativistic' Calogero-Moser Hamiltonian due to van Diejen. This amounts to a generalization of previous results concerning the Painlev\'e-Calogero correspondence to the highest level in the two hierarchies.
Keywords
Cite
@article{arxiv.1903.09738,
title = {The Elliptic Painlev\'e Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian},
author = {Masatoshi Noumi and Simon Ruijsenaars and Yasuhiko Yamada},
journal= {arXiv preprint arXiv:1903.09738},
year = {2020}
}