On Monday, November 14, 2016 at 5:36:19 AM UTC, Amri wrote: > > It would be nice to have a function for kronecker coefficients in sage. I > would be happy to implement it once I have some inputs on what would be the > best way/place. One definition of the kronecker coefficient is the > following: > > Defn. Given a sequence [la1, ...., lan] of ineteger partitions on n, the > kronecker coef of this sequence is the multiplicity of the trivial > representation the tensor product of the Specht modules corresponding to > the partitions la1, la2,...,lan. >
I'd say that there should be a function for the multiplicity of an arbitrary irreducible, not only the trivial one. > > Note: some people like to think of it slightly differently: given three > partitions la, mu and nu of n, the kronecker coefficient is the > multiplicity of V_la in V_mu \times V_nu. This coincided with the > multiplicity of the trivial rep in V_la\otimes V_\mu\otimes V_\nu (which is > the definition above). > > A quick implementation is: > sage: def kronecker_coefficient(partns): > ....: S = SymmetricFunctions(QQ).schur() > ....: pr = reduce(lambda x, y: x.itensor(y), [S[la] for la in > partns]) > ....: return pr.coefficient(Partition([sum(partns[0])])) > > This code is already in the documentation for a patch of mine at: > > https://trac.sagemath.org/ticket/17437 > > Looking forward to some feedback. > > Thanks, > Amri. > -- 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 https://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/d/optout.
