  Space-time coordinates in DSR theories with two invariant scales based on a
dispersion relation with an energy independent speed of light are introduced by
the demand, that boost and rotation generators are invariant under a
transformation from SR to DSR variables. This turns out to be equivalent to a
recent suggestion postulating the existence of plane wave solutions in DSR
theories. The momentum space representation of coordinates is derived, yielding
a noncommutative space-time and the deformed algebra.
