I have implemented some tools for working with characters of Lie groups in Sage. I intend to make a trac ticket for this, but first I posted in sage-combinat-devel for comment. I'm linking here to that post for people here interested in Lie groups. A a link to the patch and a description may be found here:
http://groups.google.com/group/sage-combinat-devel/browse_thread/thread/74ed91d5153e6022?hl=en I forgot to explain in that post how to extract the weight multiplicities from a character. Here's how you do that, using Freudenthal's algorithm. sage: G2 = WeylCharacterRing(['G',2]) sage: w = 2*G2.lattice().fundamental_weights()[0]; w (2, 0, -2) sage: chi = G2(w); chi G2("2.0.-2") sage: chi.mlist() [[(-1, 1, 0), 2], [(-1, -1, 2), 1], [(1, 1, -2), 1], <SNIP> [(0, 0, 0), 3], [(1, -2, 1), 1]] In this list, the first element of a pair is a weight, the second element its multiplicity. Apart from that, you can decompose tensor products, extract the character of a crystal, and do branching rules, all explained in the above link. Dan --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
