Expansion of Lie Groups and Representations of SL(3, C)

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Abstract
We show that in any unitary representation of SL(3, C) belonging to the principal series, the generators can be expressed as functions of the generators of a suitably chosen unitary representation of the non‐semisimple group SU(3) × T8. Both the nondegenerate and the degenerate series are considered. Since the representations of SU(3) × T8 in an SU(3) basis are known, this provides a solution to the multiplicity problem in setting up the SL(3, C) representations in an SU(3) basis.
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