The Heun Equation and the Calogero-moser-sutherland System Ii: the Perturbation and the Algebraic Solution

We justify the holomorphic perturbation for the 1particle Inozemtsev model from the trigonometric model and show the holomorphy of the eigenvalues and the eigenfuncions which are obtained by the series expansion. We investigate the relationship between the L 2 space and the nite dimensional space of certain elliptic functions, and determine the distribution of the \algebraic" eigenvalues on the nite dimensional space for the 1-particle Inozemtsev model.