Anne, > Is there now a simple way to convert > a vector in the ambient space to the root basis?
Longish answer: The "domain" of the Weyl group, the space on which it is defined to act, can be at least one of the following: 1. Ambient space 2. Root lattice 3. Coroot lattice 4. Weight lattice 5. Coweight lattice and maybe more of which I am not aware. You can recover the coefficients of simple roots of an element by taking the scalar product with fundamental coweights (not super efficient) but this works in any of the above situations with the following proviso: if the domain is the coroot or coweight lattice and you ask for ITS simple roots you get simple coroots, as elements of the coroot or coweight lattices respectively, and this "co" is applied consistently whether you ask for roots, coroots, weights or coweights. --Mark -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
