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arXiv · 1903.09738

The Elliptic Painlev\'e Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian

Masatoshi Noumi·Simon Ruijsenaars·Yasuhiko Yamada
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Abstract

The 8-parameter elliptic Sakai difference Painlev\'e equation admits a Lax formulation. We show that a suitable specialization of the Lax equation gives rise to the time-independent Schr\"odinger 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 Painlev\'e-Calogero correspondence to the highest level in the two hierarchies.

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Masatoshi Noumi, Simon Ruijsenaars, Yasuhiko Yamada. 2019-03-23. The Elliptic Painlev\'e Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian. https://doi.org/10.3842/sigma.2020.063

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