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

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dc.contributor.authorNoumi, Masatoshi
dc.contributor.authorRuijsenaars, Simon
dc.contributor.authorYamada, Yasuhiko
dc.date.accessioned2025-12-17T14:38:54Z
dc.date.issued2020
dc.description.abstractThe 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.
dc.description.sponsorshipThe 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.
dc.identifier.citationThe 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
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.063
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 39A06; 33E05
dc.identifier.otherarXiv:1903.09738
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/210785
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleThe Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік