  A recent mean-field approach to the fractional quantum Hall effect (QHE) is
reviewed, with a special emphasis on the application to single-electron
tunneling through a quantum dot in a high magnetic field. The theory is based
on the adiabatic principle of Greiter and Wilczek, which maps an incompressible
state in the integer QHE on the fractional QHE. The single-particle
contribution to the addition spectrum is analyzed, for a quantum dot with a
parabolic confining potential. The spectrum is shown to be related to the
Fock-Darwin spectrum in the integer QHE, upon substitution of the electron
charge by the fractional quasiparticle charge. Implications for the periodicity
of the Aharonov-Bohm oscillations in the conductance are discussed.
