GROUP GAMMA(2) AND THE FRACTIONAL QUANTUM HALL-EFFECT

We analyze the action of the inhomogeneous modular group Gamma (2) on the three cusps of its principal fundamental domain in the Poincare ha lf plane. From this, we obtain an exhaustive classification of the fra ctional quantum Hall numbers. This classification, in which the intege r and the fractional states appear on an equal level, is somehow simil ar to the one given by Jain. We also present some resulting remarks co ncerning direct phase transitions between the different quantum Hall s tates.