  We study a generalized Shastry-Sutherland model for the material
SrCu$_2$(BO$_3$)$_2$. Along a line in the parameter space, we can show
rigorously that the model has a first order phase transition between Dimerized
and N\'eel-ordered ground states. Furthermore, when a magnetic field is applied
in the Dimerized phase, magnetization plateaus develop at commensurate values
of the magnetization. We also discuss various aspects of the phase diagram and
properties of this model away from this exactly soluble line, which include
gap-closing continuous transitions between Dimerized and magnetically ordered
phases.
