#13838: Implementation of virtual Klebers algorithm
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #13871 #14469 | Stopgaps:
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Comment (by aschilling):
Hi Travis,
It would be good if you could implement the tensor product multiplicity
(and please call it tensor_product_multiplicity) which is formula (3.2) of
http://arxiv.org/pdf/math/9809087.pdf in order to check that the code is
giving the correct output. For nonsimply-laced types it would be the
virtual analogue of this formula. The Kleber tree gives the admissible
partitions, but to get the multiplicity one needs to sum over the product
of binomial coefficients.
Also, I think it would be better to access the VirtualKleberTree through
its own class (rather than through KleberTree). It is fine to inherit from
KleberTree, but the construction is mathematically inherently different.
For example for type `C_n^{(1)}` the construction is via the
`A_{2n-1}^{(1)}` Kleber tree and type A weights, rather than type C
weights. Since this is mostly just used in later code on rigged
configuration, I think it won't be necessary to export VirtualKleberTree
into the namespace.
Thanks for your work on this!
Anne
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Ticket URL: <http://trac.sagemath.org/ticket/13838#comment:12>
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