Abstract: The authors present a symbolic computation method for calculating the differential representations for dynamical groups, including the
right and the left differential representations, and the adjoint differential representations in the group parameter space and in its coset spaces. As an example, the corresponding representations of Lorentz SO(3,1) group with 6-parameters and 3-parameters are calculated. Especially, two different kinds of 3-parameter adjoint differential representations are obtained. At the same time, the right and the left differential representations, and the adjoint differential representations of Wigner's little group SO(2,1) and SO(3) with 6-parameters and 3-parameters are also obtained respectively. These representations are the relativistic generalization of the differential representations of the SO(3) rotation group in the Euler angles and in the polar angles. They may find their applications in the study of relativistic quantum top.

Key words: Dynamical groups, Differential representation, Lorentz group, Coset space