# Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

## Description

Abstract In this paper we present Affine.m—a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples ... Title of program: Affine.m Catalogue Id: AENB_v1_0 Nature of problem Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play a major role in a study of quantum integrable systems. Versions of this program held in the CPC repository in Mendeley Data AENB_v1_0; Affine.m; 10.1016/j.cpc.2012.06.014 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)