  The Wigner-Eckart theorem is a well known result for tensor operators of
SU(2) and, more generally, any compact Lie group. This paper generalises it to
arbitrary Lie groups, possibly non-compact. The result relies on knowledge of
recoupling theory between finite-dimensional and arbitrary admissible
representations, which may be infinite-dimensional; the particular case of the
Lorentz group will be studied in detail. As an application, the Wigner-Eckart
theorem will be used to construct an analogue of the Jordan-Schwinger
representation, previously known only for finite-dimensional representations of
the Lorentz group, valid for infinite-dimensional ones.
