  We study the Heisenberg antiferromagnet on the Shastry-Sutherland lattice
under magnetic fields, to clarify the magnetic properties of SrCu_2(BO_3)_2.
Treating magnetic excitations promoted by the field as Bose particles and using
strong coupling expansion, we derive an effective Hamiltonian for the effective
magnetic particles. Anisotropic repulsive interactions between effective
particles induce `insulating' states with a stripe SDW structure at
magnetization m/m_{sat}=1/3 and a checkerboard structure at 1/2, and thereby
form magnetization plateaus. Supersolid phases appear around insulating SDW
phases by changing the magnetic field. Nature of these supersolid phases is
discussed in detail. We also demonstrate how the geometry of the
Shastry-Sutherland lattice affects dynamical properties of magnetic excitations
significantly and makes a novel type of quintuplet (S=2) boundstates condense
for very small magnetization.
