kercl / sun

A toolkit that aims to provide several features with regards to special unitary groups, including the generation of matrix representations, decomposition of tensor products and more.

𝔰𝔲(n) Toolkit

This software package aims to provide several tools for working with representations of the Lie-algebras 𝔰𝔲(n).

The core library is written in C for efficiency and has bindings for numpy, sympy and Mathematica.

Setup

Python requirements:

• numpy
• sympy

Planned Usage

Python

import sun.numeric as sun

irrep = sun.Irrep(dynkin=[3,8])
irrep.x(i)

Mathematica

Needs["SUN`"]

irrep = Irrep[5,2,1]

X = LieAlgebraBasisMatrices[irrep, BasisType→"LoweringRaising"]
X[i]

Algorithm

The package is an implementation of the algorithm outlined in [1].

[1] Alex, Arne, et al. "A numerical algorithm for the explicit calculation of SU(N) and SL(N, C) Clebsch–Gordan coefficients." Journal of Mathematical Physics 52.2 (2011): 023507.

Planned features

• Generate irreducible representations from Dynkin labels
• Python bindings
• Mathematica bindings
• Decompose tensor products into irreducible representations
• Clebsch-Gordon coefficients