  We study the partition function for the low-energy edge excitations of the
incompressible electron fluid. On an annular geometry, these excitations have
opposite chiralities on the two edges; thus, the partition function takes the
standard form of rational conformal field theories. In particular, it is
invariant under modular transformations of the toroidal geometry made by the
angular variable and the compact Euclidean time. The Jain series of plateaus
have been described by two types of edge theories: the minimal models of the
W-infinity algebra of quantum area-preserving diffeomorphisms, and their
non-minimal version, the theories with U(1)xSU(m) affine algebra. We find
modular invariant partition functions for the latter models. Moreover, we
relate the Wen topological order to the modular transformations and the
Verlinde fusion algebra. We find new, non-diagonal modular invariants which
describe edge theories with extended symmetry algebra; their Hall
conductivities match the experimental values beyond the Jain series.
