Wolfram Language Paclet Repository

Community-contributed installable additions to the Wolfram Language

LieART/ LieART

Tools for Lie Algebras and Representation Theory

Contributed by: Robert Feger, Thomas Kephart and Robert Saskowski

LieART (Lie Algebras and Representation Theory) is a Wolfram paclet for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["LieART/LieART"]


To load the code after installation, evaluate this code:
Needs["LieART`LieART`"]

Details

LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems, and several other properties of irreducible representations. LieART's user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations are used internally and can also be used for input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast computations and low memory consumption.

Paclet Guide

Examples

In[1]:=
<< LieART`

Basic Examples (3) 

Enter the of SU(5) by its dimensional name:

In[2]:=
Irrep[SU5][Bar[10]]
Out[2]=

Decompose the tensor product of SU(3):

In[3]:=
DecomposeProduct[Irrep[SU3][3], Irrep[SU3][Bar[3]]]
Out[3]=

Decompose the of SU(5) to SU(3)⊗SU(2)⊗U(1):

In[4]:=
DecomposeIrrep[Irrep[SU5][Bar[10]], ProductAlgebra[SU3, SU2, U1]]
Out[4]=

Scope (3) 

Display the root system of SU(5) in spindle shape:

In[5]:=
RootSystem[A4, SpindleShape -> True]
Out[5]=

Show the Dynkin diagram of SO(7):

In[6]:=
DynkinDiagram[SO7]
Out[6]=

Weight diagram of SU(3) irrep 8:

In[7]:=
WeightDiagram[Irrep[SU3][8]]
Out[7]=

Publisher

LieART

Disclosures

Version History

  • 2.1.1 – 09 March 2025

License Information

GNU Lesser General Public License v3.0 only

Paclet Source

Source Metadata

  • Citation:
    • Robert Feger and Thomas W. Kephart.
      ​LieART—A Mathematica application for Lie algebras and representation theory.​
      Comput.Phys.Commun. 192 (2015), 166-195
      DOI:       10.1016/j.cpc.2014.12.023​
      e-Print:       1206.6379 [math-ph]
    • Robert Feger, Thomas W. Kephart and Robert J. Saskowski.
      ​LieART 2.0 – A Mathematica application for Lie Algebras and Representation Theory.
      ​Comput.Phys.Commun. 257 (2020), 107490
      DOI:       10.1016/j.cpc.2020.107490​
      e-Print:       1912.10969 [hep-th]