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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 063, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.063 (Mi sigma1600) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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

Masatoshi Noumia, Simon Ruijsenaarsb, Yasuhiko Yamadaa

a Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
b School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
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DOI: https://doi.org/10.3842/SIGMA.2020.063
Abstract: 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 $BC_1$ $8$-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.
Keywords: Painlevé–Calogero correspondence, elliptic difference Painlevé equation, Ruijsenaars–van Diejen Hamiltonian.
Funding agency Grant number
Japan Society for the Promotion of Science 15H03626
26287018
This work is supported by JSPS KAKENHI Grant Numbers 26287018 and 15H03626.
Received: April 20, 2020; in final form June 26, 2020; Published online July 8, 2020
Bibliographic databases:
Document Type: Article
MSC: 39A06, 33E05
Language: English
Citation: Masatoshi Noumi, Simon Ruijsenaars, Yasuhiko Yamada, “The Elliptic Painlevé Lax Equation vs. van Diejen's $8$-Coupling Elliptic Hamiltonian”, SIGMA, 16 (2020), 063, 16 pp.
Citation in format AMSBIB
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