LiE is a computer algebra system that is specialised in computations involving (reductive) Lie groups and their representations. It is publically available for free in source code and there is an online service powered by LiE at http://www-math.univ-poitiers.fr/~maavl/LiE/form.html
Citation:
@BOOK{LiE1992, author = "Marc A. A. van Leeuwen, Arjeh M. Cohen, and Bert Lisser", title = "{LiE}, A package for Lie group computations", type = "User manual" publisher = "Computer Algebra Nederland", address = "Amsterdam", year = 1992, }