Hey Joseph As far as I know, none of that functionality has been implemented in Sage. In a strongly related direction, at some point I hope to implement the classical Lie groups and what are known as geometric crystals (in the sense of Berenstein and Kazhdan). Groups of Lie type would also be something I am interested in having in Sage (at least to me, this seems to be more of what you are after). You might be interested in https://trac.sagemath.org/ticket/14901 as well (and tickets referenced therein).
Best, Travis On Wednesday, June 22, 2016 at 4:58:59 PM UTC-5, Joseph Hundley wrote: > > By "algebraic groups" I mean "split connected reductive algebraic groups > equipped with a choice of maximal torus, Borel subgroup, and > realization/pinning/epinglage." > (Though I am interested in principle in removing unnecessary hypotheses.) > > By "Chevalley generators" I mean > * elements of root subgroups (say, elements of the form x_a( expression ) > where a is a root and x_a is the fixed isomorphism from the additive group > scheme to the root subgroup) > * elements of the fixed maximal torus > * representatives for the simple reflections in the Weyl group which have > been fixed in some natural way. (The choice of x_a's gives a couple obvious > options.) > > Unless I've oversimplified here such elements generate and all the > relations among them are determined by the Cartan matrix and the matrix of > structure constants of the realization, but there is a fair amount of > book-keeping to be done. > > I'm fairly regularly interested in forming two products of elements of > root subgroups and conjugating one by the other (in exceptional groups > where this generators and relations approach is perhaps easier than a > matrix realization). Does Sage have some functionality for doing this sort > of thing that I'm unaware of? Is there more that should be added? > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
