  We study the ground state properties of a quantum antiferromagnet on the
kagome lattice in the presence of a magnetic field, paying particular attention
to the stability of the plateau at magnetization 1/3 of saturation and the
nature of its ground state. We discuss fluctuations around classical ground
states and argue that quantum and classical calculations at the harmonic level
do not lead to the same result in contrast to the zero-field case. For spin
S=1/2 we find a magnetic gap below which an exponential number of non-magnetic
excitations are present. Moreover, such non-magnetic excitations also have a
(much smaller) gap above the three-fold degenerate ground state. We provide
evidence that the ground state has long-range order of valence-bond crystal
type with nine spins in the unit cell.
