The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
Noumi, M, Ruijsenaars, S and Yamada, Y
(2020)
The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian.
Symmetry, Integrability and Geometry: Methods and Applications, 16.
063.
ISSN 1815-0659
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 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.
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Item Type:
Article
Authors/Creators:
Noumi, M
Ruijsenaars, S
Yamada, Y
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This is protected by copyright. All rights reserved. This is an open access article under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) (https://creativecommons.org/licenses/by-sa/4.0/)
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