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

TL;DR

CleGo is a software package that automates the calculation of Clebsch-Gordan coefficients for tensor products of Lie algebra representations, aiding research in particle physics and grand unified theories.

Contribution

It introduces a straightforward, explicit method for computing Clebsch-Gordan coefficients for Lie algebras A-G, including multiple tensor products and analysis tools.

Findings

Provides explicit Clebsch-Gordan coefficients for Lie algebra representations

Enables analysis of symmetry breaking in grand unified theories

Supports multiple tensor product computations

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.