  We compare the respective efficiencies of three quantization methods (group
theoretical, coherent state and geometric) by quantizing the dynamics of a free
massive particle in two-dimensional de Sitter space. For each case we consider
the realization of the principal series representation of $SO_0(1,2) $ group
and its two-fold covering SU(1,1). We demonstrate that standard technique for
finding an irreducible representation within the geometric quantization scheme
fails. For consistency we recall our earlier results concerning the other two
methods, make some improvements and generalizations.
