  An analytic form for the crossover of the conductivity tensor between two
Hall plateaux, as a function of the external magnetic field, is proposed. The
form of the crossover is obtained from the action of a symmetry group, a
particular subgroup of the modular group, on the upper-half complex
conductivity plane, by assuming that the beta-function describing the crossover
is a holomorphic function of the conductivity. The group action also leads to a
selection rule, |p_1q_2-p_2q_1|=1, for allowed transitions between Hall
plateaux with filling factors p_1/q_1 and p_2/q_2, where q_1 and q_2 are odd.
