The ground-state properties of the Heisenberg antiferromagnet on a kag
ome lattice with further-neighbor interactions are discussed. The clas
sical ground states are described as spiral phases of an equivalent sq
uare lattice with a basis, and quantum fluctuations are incorporated b
y means of a rotationally invariant Schwinger-boson approach. The quas
iparticle dispersion relations have the correct zero-mode structure, w
ithout the pathologies present in the standard spin-wave approximation
. For the nearest-neighbor S = 1/2 model the theory predicts an ordere
d ground state, although with a largely reduced magnetization of only
18% of the classical value. Implications of the results for the low-te
mperature thermodynamics of the stacked S = 3/2 kagome antiferromagnet
SrCr8-xGa4+xO19 are also discussed.