The anti ferromagnetic Heisenberg model on the frustrated Shastry-Sutherlan
d lattice is studied by a mapping onto spinless fermions carrying one quant
um of statistical flux. Using a mean-field approximation these fermions pop
ulate the bands of a generalized Hofstadter problem. Their filling leads to
the magnetization curve. For SrCu2(BO3)(2) we reproduce plateaus at 1/3 an
d 1/4 of the saturation moment and predict a new one at 1/2. Gaussian fluct
uations of the gauge field are shown to be massive at these plateau values.