E_6 unification model building III. Clebsch-Gordan coefficients in E_6 tensor products of the 27 with higher dimensional representations

Abstract

$E_6$ is an attractive group for unification model building. However, the complexity of a rank 6 group makes it non-trivial to write down the structure of higher dimensional operators in an $E_6$ theory in terms of the states labeled by quantum numbers of the Standard Model gauge group. In this paper, we show the results of our computation of the Clebsch-Gordan coefficients for the products of the {\bf 27} with irreducible representations of higher dimensionality: $78$, $351$, $351^{\prime }$, ${\bf \ol{351}}$, and ${\bf \ol{351^\prime}}$. Application of these results to $E_6$ model building involving higher dimensional operators is straightforward.

44 pages, 31 tables