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We derive the matrix elements of generators of unitary irreduciblerepresentations of SL(2,C) with respect to basis states arising from adecomposition into irreducible representations of SU(1,1). This is done withregard to a discrete basis diagonalized by J^3 and a continuous basisdiagonalized by K^1, and for both the discrete and continuous series ofSU(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 anddifferential operators have a similar structure in all five cases. The statesare defined explicitly and related to SU(1,1) and SU(2) matrix elements.

Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases