<span>WignerEckart</span>theorem and <span>JordanSchwinger</span>representation for infinite-dimensional representations of the Lorentz group

The WignerEckart theorem is a well known result for tensor operators of ${\mathrm{SU}}(2)$ 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 WignerEckart theorem will be used to construct an analogue of the JordanSchwinger representation, previously known only for finite-dimensional representations of the Lorentz group, valid for infinite-dimensional ones.

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Introduction
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Representation theory {#sec:representation_theory}
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Tensor Operators {#sec:tensor_operators}
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Concluding remarks
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The author would like to thank Florian Girelli for introducing him to the topic and providing useful insights.

Notation
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<span>Clebsch–Gordan</span> coefficients {#app:CG}
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Tridiagonal matrices {#app:tridiagonal}
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{'source': 'arXiv_out/1509'}