  We study the low-lying excitations of a quantum-Hall sample that has
undergone edge reconstruction such that there exist three branches of chiral
edge excitations. Among the interaction processes that involve electrons close
to the three Fermi points is a new type of Umklapp-scattering process which has
not been discussed before. Using bosonization and a refermionization technique,
we obtain exact results for electronic correlation functions and discuss the
effect Umklapp scattering has on the Luttinger-liquid properties of
quantum-Hall edges.
