Elliptic Linear Problem for Calogero-Inozemtsev Model and Painleve VI Equation
arXiv:hep-th/0310260 · doi:10.1023/B:MATH.0000032753.97756.94
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