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

TL;DR

Affine.m is a Mathematica package that facilitates computations in the representation theory of finite-dimensional and affine Lie algebras, focusing on weight multiplicities, branching, and tensor products, with applications in physics.

Contribution

The paper introduces Affine.m, a new computational tool implementing algorithms for Lie algebra representations within Mathematica, enhancing efficiency and accessibility.

Findings

Successfully computes weight multiplicities in various modules

Supports branching rules and tensor product decompositions

Demonstrates applications in physics problems

Abstract

In this paper we present Affine.m - program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. Algorithms are based upon the properties of weights and Weyl symmetry. The most important problems for us are the ones, concerning computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras.