> Yes, it also exists for any Cartan type, but my impression was that then > it is called Lusztig involution. My plan is indeed to eventually implement > the Lusztig involution in CrystalOfTableauxElements. What do you think?
That sounds like the right approach. Actually the Lusztig involution would be pretty easy to implement for irreducible crystals and would give a way of checking the correctness of the patch in question. > I don't have the details on top of my head, so I'll just speak vaguely > here. Unless the algorithms are basically identical, it seems very > reasonable to have a generic (type-free?) implementation in > CrystalOfTableauxElements using the crystal structure, and a > specialized implementation in Tableaux using the combinatorics of > tableaux. And to include some tests that compare the results and check > their consistency! I am agreeing with this. For crystals, the algorithm is as follows. There is an involution of the indices which for type A is i --> r+1-i but for other types may be trivial. Anyway call this i -> i'. Now if v is in the crystal C, find a path from the highest weight vector to v. Then start with the lowest weight vector and find the symmetrical path to some vertex, where the symmetry replaces e(i) -> f(i'). Where you end up is the involution of v. Dan -- 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.
