  We develop a formalism suitable for the study of transport properties of
coherent multiple dots which captures and explains the experimentally observed
features in terms of spectral properties of the system. The multiplet structure
of the transmission spectrum and the role of the intra-dot and inter-dot
Coulomb interaction are pointed out. The evolution of the sub-peaks with the
magnetic field in the quantum Hall regime is shown. We suggest a specific
oscillatory behaviour of the Hall resistance in strong magnetic field which can
be experimentally tested.
