The branch conductance as well as the conductance sum rule for the hierarchical edge channel currents of a fractional-quantum-Hall-effect state are derived analytically within the Haldane-Halperin hierarchy scheme. The comparison of our result and those of previous works is discussed. We provide also an intuitive interpretation for the heirarchical drift velocities of the edge excitations which are different for different edge channels.

• Received 17 February 1994

DOI:https://doi.org/10.1103/PhysRevB.50.2232