  The antiferromagnetic Heisenberg model on the frustrated Shastry-Sutherland
lattice is studied by a mapping onto spinless fermions carrying one quantum of
statistical flux. Using a mean-field approximation these fermions populate the
bands of a generalized Hofstadter problem. Their filling leads to the
magnetization curve. For SrCu_2(BO_3)_2 we reproduce plateaus at 1/3 and 1/4 of
the saturation moment and predict a new one at 1/2. Gaussian fluctuations are
shown to be massive at these plateau values.
