The Γ9 × (g + 2h) Jahn-Teller Hamiltonian

The sixfold degenerate irreducible representation Γ9 corresponds to the highest degeneracy that a point group can sustain. The Hamiltonian describing the Jahn-Teller instability is of type Γ9 × (g + 2h). The general solutions of this Hamiltonian are presented, and various coupling schemes are discussed.