On the relation between polynomial deformations of sl(2,R) and   quasi-exactly solvability
  A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the finite-dimensional representations and differential realizations of such deformations is illustrated on the sextic oscillator as well as on the second harmonic generation. 
N. Debergh