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

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...

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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
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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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Noumi, Masatoshi
Ruijsenaars, Simon
Yamada, Yasuhiko
author_facet Noumi, Masatoshi
Ruijsenaars, Simon
Yamada, Yasuhiko
citation_txt 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
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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 amounts to a generalization of previous results concerning the Painlevé-Calogero correspondence to the highest level in the two hierarchies.
first_indexed 2026-03-16T11:08:37Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-16T11:08:37Z
publishDate 2020
publisher Інститут математики НАН України
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spelling Noumi, Masatoshi
Ruijsenaars, Simon
Yamada, Yasuhiko
2025-12-17T14:38:54Z
2020
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
1815-0659
2020 Mathematics Subject Classification: 39A06; 33E05
arXiv:1903.09738
https://nasplib.isofts.kiev.ua/handle/123456789/210785
https://doi.org/10.3842/SIGMA.2020.063
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 amounts to a generalization of previous results concerning the Painlevé-Calogero correspondence to the highest level in the two hierarchies.
The research reported in this article was initiated during a visit of S.R. to the Department of Mathematics of Kobe University. He would like to thank the Department for its hospitality and financial support. This work is supported by JSPS KAKENHI Grant Numbers 26287018 and 15H03626.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
Article
published earlier
spellingShingle The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
Noumi, Masatoshi
Ruijsenaars, Simon
Yamada, Yasuhiko
title The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
title_full The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
title_fullStr The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
title_full_unstemmed The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
title_short The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
title_sort elliptic painlevé lax equation vs. van diejen's 8-coupling elliptic hamiltonian
url https://nasplib.isofts.kiev.ua/handle/123456789/210785
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