E-6 unification model building. I. Clebsch-Gordan coefficients of 27 circle times(27)over-bar

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 c oefficients for the product (100000)x(000010), where (100000) is the fundam ental 27-dimensional representation of E-6 and (000010) is its charged conj ugate. The results are presented in terms of the dominant weight states of the irreducible representations in this product. These results are necessar y for the group analysis of E-6 operators also involving higher representat ions, which is the next step in this project. In this paper we apply the re sults to the construction of the operator 27(3). (C) 2000 American Institut e of Physics. [S0022-2488(00)05407-4].