Quasi-exact solvability of Inozemtsev models

Finite-dimensional spaces which are invariant under the action of the Hamiltonian of the BC_N Inozemtsev model are introduced, and it is shown that higher commuting operators also preserve the finite-dimensional spaces. The relationship between the finite-dimensional spaces of the BC_N Inozemtsev models and the theta-type invariant spaces of the BC_N Ruijsenaars models is clarified. The degeneration of the BC_N Inozemtsev models and the correspondence of their invariant spaces are considered.