This looks really awesome Dan. It's really great you are working on this. Is there any functionality planned for products of GL(1)'s (for example)?
On Sat, Apr 26, 2008 at 3:49 PM, Daniel Bump <[EMAIL PROTECTED]> wrote: > > > 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 -~----------~----~----~----~------~----~------~--~---
