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.

Reply via email to