On Monday, November 14, 2016 at 10:44:35 AM UTC, Amri wrote: > > But you just add the "arbitrary irreducible" to your list: > > mult of la in mu\otimes nu = mult of triv in mu\otimes\nu\otimes la > > there is complete symmetry between the parameters. >
Well, this still does not imply that one doesn't want la as an extra parameter for the function, even if only for convenience. (imagine a user that has a bit less representation theory of S_n loaded in his/her head than you :-)) > On Monday, November 14, 2016 at 3:54:24 PM UTC+5:30, Dima Pasechnik wrote: >> >> >> >> 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.
