LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory

TL;DR

LieART 2.0 is an enhanced Mathematica tool that streamlines complex computations in Lie algebra and representation theory, including tensor products and subalgebra branching, with expanded data tables and user-friendly features.

Contribution

It introduces new computational procedures and extended tables in LieART 2.0, enabling seamless calculations of root systems, weight systems, tensor products, and branching rules for a wide range of Lie algebras.

Findings

Includes branching rules for all classical and exceptional Lie algebras up to rank 15.

Provides extended tables of properties, tensor products, and branching rules.

Maintains user-friendly interface with new features and procedures.

Abstract

We present LieART 2.0 which contains substantial extensions to 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. The basic procedure is unchanged: it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the supplementary material for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15.