$E_6$ unification model building I: Clebsch-Gordan coefficients of $27\otimes \ol{27}$

Details $E_6$ unification model building I: Clebsch-Gordan coefficients of $27\otimes \ol{27}$ $E_6$ unification model building I: Clebsch-Gordan coefficients of $27\otimes \ol{27}$

1999-12-15

arxiv.org/abs/hep-ph/9912365v1

J.Math.Phys. 41 (2000) 4808-4816

Physics

High Energy Physics

High Energy Physics - Phenomenology

11 pages, LaTeX

Scientific paper

10.1063/1.533380

In an effort to develop tools for grand unified model building for the Lie group $E_6$, in this paper we present the computation of the Clebsch-Gordan coefficients for the product (100000) $\otimes$ (000010), where (100000) is the fundamental 27-dimensional representation of $E_6$ and (000010) is its charged conjugate. The results are presented in terms of the dominant weight states of the irreducible representations in this product. These results are necessary for the group analysis of $E_6$ operators involving also higher representations, which is the next step in this project. In this paper we apply the results to the construction of the operator ${\bf 27}^3$.

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