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In $E(6)$ inspired models of supersymmetry, the inclusion of Lie subgroups $$ SO(10) \times U(1) \hookrightarrow E_6 $$ is important object of interest. See here for my motivating example.

In particular, paper uses the decomposition of some irreducible representations of $E(6)$ into its irreducible sub-representations with respect to the subgroup $SO(10) \times U(1)$.

Such rules as these are called "branching rules". Does there exist a single branching rule of the general $E(6)$ irreducible representation to its irreducible $SO(10) \times U(1)$-irreducible subrepresentations? What is a best reference?

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Maybe the following reference will be useful: https://www.sciencedirect.com/science/article/pii/0370157381900922 (Group theory for unified model building, by R.Slansky).

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