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The Wigner-Eckart theorem is a well known result for tensor operators ofsu(2) and, more generally, any compact Lie algebra. In this paper the theoremwill be generalized to the particular non-compact case of sl(2,R). In order todo so, recoupling theory between representations that are not necessarilyunitary will be studied, namely between finite-dimensional andinfinite-dimensional representations. As an application, the Wigner-Eckarttheorem will be used to construct an analogue of the Jordan-Schwingerrepresentation, previously known only for representations in the discreteclass, which also covers the continuous class.

Wigner-Eckart theorem for the non-compact algebra sl(2,R)