The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Noumi, Masatoshi, Ruijsenaars, Simon, Yamada, Yasuhiko
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210785
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian. Masatoshi Noumi, Simon Ruijsenaars and Yasuhiko Yamada. SIGMA 16 (2020), 063, 16 pages

The 8-parameter elliptic Sakai difference Painlevé equation admits a Lax formulation. We show that a suitable specialization of the Lax equation gives rise to the time-independent Schrödinger equation for the BC₁ 8-parameter 'relativistic' Calogero-Moser Hamiltonian due to van Diejen. This...