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.
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.
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