Elliptic Linear Problem for Calogero-Inozemtsev Model and Painleve VI Equation

Abstract

We introduce $3N\times 3N$ Lax pair with spectral parameter for Calogero-Inozemtsev model. The one degree of freedom case appears to have $2\times 2$ Lax representation. We derive it from the elliptic Gaudin model via some reduction procedure and prove algebraic integrability. This Lax pair provides elliptic linear problem for the Painlev{é} VI equation in elliptic form.

LaTeX, 13 pages

References in corpus (1)

• Hitchin Systems - Symplectic Hecke Correspondence and Two-dimensional Version

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