It looks like Sage is constructing the wrong crystals for the two spin weights. D5 does have two irreducible representations of dimensions 210 and 126 but their highest weights are not the spin weights s1=(1/2,1/2,1/2,1/2,1/2) and s2=(1/2,1/2,1/2,1/2,-1/2) which are the two fundamental weights. Instead the highest weights of the representations with these degrees 210 and 126 are s1+s2 and 2*s1.
This appears to me to be a bug in the crystal code. Daniel Bump On Thursday, February 11, 2021 at 9:30:15 AM UTC-8 axio...@yahoo.de wrote: > I am confused about the following result: > > sage: ct = CartanType(["D", 5]) > sage: L = RootSystem(ct).weight_lattice() > sage: La = L.fundamental_weights(); > sage: [L.weyl_dimension(wt) for wt in La] > [10, 45, 120, 16, 16] > sage: [crystals.HighestWeight(wt).q_dimension().subs(q=1) for wt in La] > [10, 45, 120, 210, 126] > > Am I doing something wrong or is this a bug? I would expect the former > dimensions, but I am not versed enough in the theory to be sure that I did > not make a mistake myself. The discrepancy seems to occur only with type D. > > All the best, > > Martin > -- 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 sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/aab7c0f2-047e-46cd-9dde-887d597ea41fn%40googlegroups.com.
