The extended-variable ("ballooning") representation, commonly used for the study of short wavelength plasma modes in a toroidal magnetic equilibrium, is generalised to include: i) the effect of a differential toroidal rotation ii) non linear terms in the mode amplitude. These results are obtained by relating this representation to the irreducible representations of the relevant invariance group, which is shown to be a discrete Abelian subgroup of the Heisenberg group.