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Register a new userThe Elliptic Painleve Lax Equation vs. van Diejens 8-Coupling Elliptic Hamiltonian
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The 8-parameter elliptic Sakai difference Painleve equation admits a Lax formulation. We show that a suitable specialization of the Lax equation gives rise to the time-independent Schrodinger 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 Painleve-Calogero correspondence to the highest level in the two hierarchies.
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