On Wed, Nov 16, 2016 at 08:09:20AM -0800, Travis Scrimshaw wrote:
> Perhaps Andrew can weigh in on putting Kronecker coefficients with
> partition tuples, but it feels somewhat artificial to me. Instead, I
> like the explicitness of the syntax
> la.kronecker_coefficient(mu, nu)
> and/or having some (lazily imported) global namespace function of
> kronecker_coefficient (both taking arbitrary inputs representing the
> multiplicity of lambda in a longer tensor product).
Just throwing my 2 cents in the air:
In a perfect world, we would have a natural entry point for everything
related to the representation theory of the tower of symmetric
groups. Something like
sage: T = SymmetricGroups().representation_theory()
Then, a natural location could be:
sage: T.kronecker_coefficient(...)
We could also argue that kronecker_coefficients are deeply connected
with symmetric functions. For the case of three arguments lambda, mu,
nu, the natural location would be
sage: s = SymmetricFunctions().Schur()
sage: s.structure_coefficient(lambda, mu, nu)
For the general case, we could think of:
sage: s.structure_coefficient_nary([...], nu)
sage: s.structure_coefficient_nary([...])
Both of the above have the advantage of fitting into a generic API for
all our algebras (e.g. NCSF, ...).
In case we want to help the users explicitly searching for the keyword
kronecker, we could have an alias:
sage: SymmetricFunctions().kronecker_coefficient([....], ...)
One other source of inspiration as well could be the API that GAP is
using for computations with group characters.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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