Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 038, 17 pages      math.CA/0703057      https://doi.org/10.3842/SIGMA.2007.038
Contribution to the Vadim Kuznetsov Memorial Issue

Towards Finite-Gap Integration of the Inozemtsev Model

Kouichi Takemura
Department of Mathematical Sciences, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan

Received October 31, 2006, in final form February 07, 2007; Published online March 02, 2007

Abstract
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.

Key words: finite-gap integration; Inozemtsev model; Heun's equation; Darboux transformation.

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