LieART 2.0--An Improved Way to Compute Branching Rules

Abstract

In this thesis, 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. LieART 2.0 can now handle all classical and exceptional Lie algebras up through rank 15. 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. Some extended tables of branching rules of irreducible representations are included in the supplementary material for use without Mathematica software.