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

Anton Nazarov
Journal / Anthology

Computer Physics Communications
Year: 2012
Volume: 183
Page range: 2480–2493

In this paper we present Affine.m—a program for computations in representation theory of finitedimensional 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 of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras.

*Applied Mathematics
*Applied Mathematics > Computer Science
*Mathematics > Algebra
*Science > Physics

Lie algebra, Affine Lie algebra, Kac–Moody algebra, Root system, Weights, Irreducible modules, CFT, integrable systems