  We derive the matrix elements of generators of unitary irreducible
representations of SL(2,C) with respect to basis states arising from a
decomposition into irreducible representations of SU(1,1). This is done with
regard to a discrete basis diagonalized by J^3 and a continuous basis
diagonalized by K^1, and for both the discrete and continuous series of
SU(1,1). For completeness we also treat the more conventional SU(2)
decomposition as a fifth case. The derivation proceeds in a functional /
differential framework and exploits the fact that state functions and
differential operators have a similar structure in all five cases. The states
are defined explicitly and related to SU(1,1) and SU(2) matrix elements.
