A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients

TL;DR

This paper introduces a numerical algorithm for calculating SU(N) and SL(N,C) Clebsch-Gordan coefficients using Gelfand-Tsetlin patterns, facilitating computational applications in representation theory.

Contribution

The paper presents a novel, efficient algorithm for explicit numerical calculation of Clebsch-Gordan coefficients for SU(N) and SL(N,C), including implementation details.

Findings

Algorithm successfully computes coefficients for various N

Provides a computer code for practical use

Applicable to representation theory problems

Abstract

We present an algorithm for the explicit numerical calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients, based on the Gelfand-Tsetlin pattern calculus. Our algorithm is well-suited for numerical implementation; we include a computer code in an appendix. Our exposition presumes only familiarity with the representation theory of SU(2).