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[Licence| Download | New Version Template] aenb_v1_0.tar.gz(1021 Kbytes)
Manuscript Title: Affine.m - Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras
Authors: Anton Nazarov
Program title: Affine.m
Catalogue identifier: AENB_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 183(2012)2480
Programming language: Mathematica.
Computer: i386-i686, x86_64.
Operating system: Linux, Windows, MacOS, Solaris.
RAM: 5-500 Mb
Keywords: Mathematica, Lie algebra, affine Lie algebra, Kac-Moody algebra, root system, weights, irreducible modules, CFT, Integrable systems.
PACS: 02.20.Sv, 02.20.Tw.
Classification: 4.2, 5.

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.

Solution method:
We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent algorithm based on generalization of Weyl character formula. We also offer alternative implementation based on Freudenthal multiplicity formula which can be faster in some cases.

Computational complexity grows fast with the rank of an algebra, so computations for algebras of ranks greater than 8 are not practical.

Unusual features:
We offer the possibility of using a traditional mathematical notation for the objects in representation theory of Lie algebras in computations if Affine.m is used in the Mathematica notebook interface.

Running time:
From seconds to days depending on the rank of an algebra and the complexity of a representation.