Geodesic
The Elliptic Painlevé Lax Equation vs. van Diejen's $8$-Coupling Elliptic Hamiltonian
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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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: Ruijsenaars–van Diejen Hamiltonian.
Mots-clés : Painlevé–Calogero correspondence, elliptic difference Painlevé equation 
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     author = {Masatoshi Noumi and Simon Ruijsenaars and Yasuhiko Yamada},
     title = {The {Elliptic} {Painlev\'e} {Lax} {Equation} vs. van {Diejen's} $8${-Coupling} {Elliptic} {Hamiltonian}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a62/}
}
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Masatoshi Noumi; Simon Ruijsenaars; Yasuhiko Yamada. The Elliptic Painlevé Lax Equation vs. van Diejen's $8$-Coupling Elliptic Hamiltonian. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a62/

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