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.

arXiv comment44 pages, 31 tables

Cited by in corpus (6)

• Gauge boson families in grand unified theories of fermion masses: E_6^4 x S_4
• Fermion masses in E_6 grand unification with family permutation symmetries
• E_6 unification model building II. Clebsch-Gordan coefficients of 78$\otimes$78
• CleGo: A package for automated computation of Clebsch-Gordan coefficients in Tensor Product Representations for Lie Algebras A - G
• A Supersymmetric Grand Unified Model with Noncompact Horizontal Symmetry
• SOSpin, a C++ library for Yukawa decomposition in SO(2N) models