Representation Functions for SU(3)

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Abstract
``Euler'' decomposition for SU(3) has been found by analytic continuation from the ``Euler'' decomposition of SU(2, 1), which is based on the factorization SU(2, 1) = SU(2) × Au × A × SU(2) derived by Hillion [Au ∼ U(1) and A is one‐parameter subgroup of the V‐spin subgroup.] For the degenerate case the SU(3) representation functions can be found by transforming to a new basis where the V‐spin subgroup is diagonal. The result is a sum of products, each product containing two D‐functions, one d‐function, and an exponential function exp [imχ]. As is well known, every representation D(p, q) can be reduced from the direct product D(p, 0) × D(q, q). The nondegenerate representation functions can then be directly written down using the SU(3) CG coefficients, which are relatively simple for the above‐mentioned case.

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