Thanks, Travis. I guess I am inclined to try to build this thing and see who is interested in it. The ticket you linked is very helpful to me.
I'm interested to know more about your plans for Lie groups and Groups of Lie type. In some sense it seems to me that the objects I'm really working with are Group schemes defined using a certain presentation. If I have a group scheme I can take real points to get a lie group or points over a finite field to get a finite group of Lie type. On the other hand depending on what one wants to do with the Lie group/FGLT, this might have little to nothing to do with how one wants to think about them. Joe On Thursday, June 23, 2016 at 2:44:47 AM UTC-4, Travis Scrimshaw wrote: > > 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
