  In the search for spin-1/2 kagome antiferromagnets, the mineral volborthite
has recently been the subject of experimental studies [Hiroi et al.,2001]. It
has been suggested that the magnetic properties of this material are described
by a spin-1/2 Heisenberg model on the kagome lattice with spatially anisotropic
exchange couplings. We report on investigations of the Sp(N) symmetric
generalisation of this model in the large N limit. We obtain a detailed
description of the dependence of possible ground states on the anisotropy and
on the spin length S. A fairly rich phase diagram with a ferrimagnetic phase,
incommensurate phases with and without long range order and a decoupled chain
phase emerges.
