  Let (\Gamma,d) be the 3D-calculus or the 4D_{\pm}-calculus on the quantum
group SU_q(2). We describe all pairs (\pi, F) of a *-representation \pi of
O(SU_q(2)) and of a symmetric operator F on the representation space satisfying
a technical condition concerning its domain such that there exist a
homomorphism of first order differential calculi which maps dx into the
commutator [iF,\pi(x)] for x\in O(SU_q(2)). As an application commutator
representations of the 2-dimensional left-covariant calculus on Podles' quantum
2-sphere S^2_{qc} with c=0 are given.
