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

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

2003-10-28

arxiv.org/abs/hep-th/0310260v1

Lett.Math.Phys. 67 (2004) 153-165

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 13 pages

Scientific paper

10.1023/B:MATH.0000032753.97756.

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{\'e} VI equation in elliptic form.

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