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

Understand

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.