Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry

Inozemtsev models are classically integrable multi-particle dynamical systems related to Calogero-Moser (CM) models. Because of the additional q6 (rational models) or sin 22q (trigonometric models) potentials, their quantum versions are not exactly solvable, in contrast to CM models. We show that quantum Inozemtsev models can be deformed to be a widest class of partly solvable (or quasi-exactly solvable) multi-particle dynamical systems. They posses N-fold supersymmetry, which is equivalent to quasi-exact solvability. A new method for identifying and solving quasi-exactly solvable systems, the method of pre-superpotential, is presented. (author)