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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