LiE (http://www-math.univ-poitiers.fr/~maavl/LiE/) is a computer algebra package for computations with reductive Lie groups and their representations. It was developed under the direction of Arjeh Cohen (http://www.win.tue.nl/~amc/) by the computer algebra group at the Centre for Mathematics and Computer Science in Amsterdam.
From a description written by Marc van Leeuwen (http://www-math.univ-poitiers.fr/~maavl/): "The package offers an extensive library of functions implementing fundamental algorithms related to the theory of reductive Lie groups, in the following areas: root systems, the Weyl group and its action on the root and weight lattices, semisimple elements and their centralizers, highest weight modules, finite dimensional representations, characters, decompositions of tensor products, restrictions to subgroups (branching), symmetric group characters, symmetric and alternating tensor powers, and more general plethysms."
LiE is free software.
A Sage package lie-*.spkg can be downloaded from [http://www.sagemath.org/packages/optional/]. At the time of writing, the latest version is lie-2.2.2.p3.spkg.
