LieART

LieART (Lie Algebras and Representation Theory) is a Mathematica application for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. 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 a low memory consumption. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15. Extensive tables of properties, tensor products and branching rules of irreducible representations are included in the appendix of the associated publication.

New Version: LieART 2.1 introducing DynkinDiagram[algebra] and ExtendedDynkinDiagram[algebra] for generating Dynkin diagrams and WeightDiagram[su3Irrep] for the display of SU(3) weight diagrams.

LieART 2.0 is associated with arXiv:1912.10969 [hep-th]
(There are some minor disagreements between the LieART 2.0.2 code and the published CPC paper that describes it. The code has been altered to better align the normalizations and branching rules used by Slansky and Yamatsu. The code should be seen as taking precedent over the paper.)

LieART 1.x is associated with arXiv:1206.6379 [math-ph]

Installation

Automatic Installation

Start Mathematica and in the front end select the menu entry File → Install.. In the appearing dialog select Application as Type of Item to Install and the archive in the open file dialog from Source. (It is not necessary to extract the archive since Mathematica does this automatically.) Choose whether you want to install LieART for an individual user or system wide. For a system-wide installation you might be asked for the superuser password.

Manual Installation

If problems with the automatic installation occur, proceed with a manual one as follows:

Extract the archive to the subdirectory Applications of the directory to which $UserBaseDirectory is set for a user-only installation. For a system-wide installation place it in the subdirectory AddOns/Applications of $InstallationDirectory. Restart Mathematica to allow it to integrate LieART's documentation it its help system.

Documentation

The documentation of LieART is integrated in Mathematica's help system. After restarting Mathematica the following path should lead to LieART's documentation:

Help → Wolfram Documentation → Add-Ons & Packages (at the bottom) → LieART, Button labeled Documentation

(Alternatively, a search for LieART (with correct case) in the Documentation Center leads to the same page.) The displayed page serves as the documentation home of LieART and includes links to the descriptions of its most important functions.

The documentation of LieART includes a Quick Start Tutorial for the impatient, which can be found almost on the top right of LieART's documentation home under the drop down Tutorials.

Tables of representation properties, tensor products and branching rules generated by LieART can be found in the section Tables at the bottom of LieART's documentation home.

LaTeX Package

LieART comes with a LaTeX package that defines commands to display irreps, roots and weights properly. The style file (lieart.sty) can be found in the subdirectory latex/ of the LieART project tree. Please copy it to a location where your LaTeX installation can find it, which may be the directory of your LaTeX source file using it.

Contact

License

Copyright (C) 2012-2020 Robert Feger, Robert Saskowski

This application is subject to the GNU Lesser General Public License (LGPL). For details see COPYING and COPYING.LESSER that come with the application.