CleGo: A package for automated computation of Clebsch-Gordan coefficients in Tensor Product Representations for Lie Algebras A - G

Abstract

We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward approach (which is slower and more memory-consumptive than the standard methods to just calculate dimensions of the tensor product decomposition) produces Clebsch-Gordan coefficients that are of interest for instance in discussing symmetry breaking in model building for grand unified theories. For that purpose, multiple tensor products have been implemented as well as means for analyzing the resulting effective operators in particle physics.

arXiv comment44 pages, 2 figures

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• WHIZARD: Simulating Multi-Particle Processes at LHC and ILC
• $E_6$ unification model building I: Clebsch-Gordan coefficients of $27\otimes \ol{27}$
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