Hi Anne, It seems my example was an over simplification.
Start with the tensor power of a finite type crystal or representation. This is a linear combination of weights with integer coefficients. I have two methods for replacing each integer coefficient by a polynomial. Each polynomial has positive integer coefficients and evaluated at 1 gives the original integer. One method using the LiE package and plethysm in particular. The other polynomial uses the energy function. The actual command (which I simplified above) is: sage: sum( L.term( a.weight(), q^(a.energy_function() ) ) for a in hw ) where L now has coefficients polynomials in q. One possibility would be to use classical_decomposition as you suggest and then construct the crystal isomorphisms explicitly. Then using this isomorphism on words I can construct the energy function on words in the ordinary crystal. At the moment I am restricting attention to KR crystals whose classical decomposition is irreducible. I have not understood if I also need to restrict to level 0. On Saturday, November 23, 2013 10:16:39 PM UTC, Anne Schilling wrote: > > Hi Bruce, > > If you are only interested in the classical weight, then you can do > > sage: C = KirillovReshetikhinCrystal(['A',1,1],1,2) > sage: B = C.classical_decomposition() > sage: T = TensorProductOfCrystals(*[B]*3) > sage: L = CombinatorialFreeModule(ZZ,B.weight_lattice_realization()) > sage: hw = [a for a in T if a.is_highest_weight()] > sage: sum( L.term( a.weight(), 1 ) for a in hw ) > B[(3, 3)] + 3*B[(4, 2)] + 2*B[(5, 1)] + B[(6, 0)] > > Best wishes, > > Anne > > On 11/23/13 2:13 AM, Bruce wrote: > > Sorry about being difficult. > > > > Here is one command: > > > > lie.p_tensor(3,[2],'A1') > > > > Here is an alternative: > > > > C = KirillovReshetikhinCrystal(['A',1,1],1,2) > > L = CombinatorialFreeModule(ZZ,C.weight_lattice_realization()) > > T = TensorProductOfCrystals(*[C]*3) > > hw = [ a for a in T if a.e(1) == None ] > > sum( L.term( a.weight(), 1 ) for a in hw ) > > > > I would like to convince sage (in this simplified example) that these > are "the same". > > > > Thank you for your patience. > > > > On Saturday, November 23, 2013 7:28:26 AM UTC, Nicolas M. Thiery wrote: > > > > On Fri, Nov 22, 2013 at 08:09:25AM -0800, Bruce wrote: > > > Here is the result of the first calculation (using the KR > crystal) and its > > > parent: > > > > Please, not the result but the command (or a simplified version) > > producing the result! Otherwise one has to reconstruct the command > to > > play with the objects :-) > > > > Cheers, > > Nicolas > -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
