LieART -- A Mathematica Application for Lie Algebras and Representation Theory

TL;DR

LieART is a Mathematica tool that simplifies complex calculations in Lie algebra and representation theory, including tensor products and subalgebra branching, with a focus on usability and efficiency.

Contribution

It introduces a user-friendly Mathematica application capable of handling all classical and exceptional Lie algebras for various computations in representation theory.

Findings

Supports all classical and exceptional Lie algebras

Provides fast computations using Weyl reflection group

Includes extensive tables of properties and branching rules

Abstract

We present the Mathematica application LieART (Lie Algebras and Representation Theory) 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. Extensive tables of properties, tensor products and branching rules of irreducible representations are included in the appendix.