Towards Finite-Gap Integration of the Inozemtsev Model

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The Inozemtsev model is considered to be a multivaluable generalization of Heun's equation. We review results on Heun's equation, the elliptic Calogero-Moser-Sutherland model and the Inozemtsev model, and discuss some approaches to the finite-gap integration for multivariable models.
This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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