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

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.

29 pages, 7 figures, updated to match published version

References in corpus (5)

• Tensor powers for non-simply laced Lie Algebras $B_2$ case
• Recursive algorithm and branching for nonmaximal embeddings
• Introducing LambdaTensor1.0 - A package for explicit symbolic and numeric Lie algebra and Lie group calculations
• String Functions for Affine Lie Algebras Integrable Modules
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