#16451: Implement tensor product of cystals categories and a better search for
highest weight elements
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: combinatorics | Resolution:
Keywords: crystals, tensor | Merged in:
products | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | aecbe5464d9002ecdcebf66cc78e639c3bc74f60
public/crystals/highest_weight_tensor-16451| Stopgaps:
Dependencies: |
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Changes (by tscrim):
* status: new => needs_review
* commit: => aecbe5464d9002ecdcebf66cc78e639c3bc74f60
* branch: => public/crystals/highest_weight_tensor-16451
Old description:
> Currently in a tensor product of crystals, we search through all elements
> and filter. However if given a highest weight element in a tensor product
> `a (x) b`, then `b` must be highest weight. This means we can use a
> backtracing algorithm to find all highest weight elements which this
> ticket implements.
New description:
Currently in a tensor product of crystals, we search through all elements
and filter. However if given a highest weight element in a tensor product
`a (x) b`, then `b` must be highest weight. This means we can use a
backtracing algorithm to find all highest weight elements which this
ticket implements.
This first implements the categories of tensor products of crystals
(currently all crystal subcategories are monoidal under tensor products).
This also changes the output of the current `highest_weight_vectors()` to
return a tuple since we don't want to allow modifications to the output of
a `@cached_method`.
--
Comment:
As far as I can tell, this is independent of #16001.
Nicolas, can you make a quick check to make sure I'm doing everything
correctly? If I am, I think I've found a bug for `Modules`:
{{{
sage: Modules(QQ).TensorProducts()
Category of objects
}}}
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=a68457fa8206a424d79d96479ec776952f9b461b
a68457f]||{{{Implemented a better search for highest weight elements in
tensor products.}}}||
||[http://git.sagemath.org/sage.git/commit/?id=53ebc56f366384256106570d6031989ab981360d
53ebc56]||{{{Created tensor product of crystals category.}}}||
||[http://git.sagemath.org/sage.git/commit/?id=81adbde363973f2756afb41cb3e6d897db639c95
81adbde]||{{{Implemented other tensor product categories.}}}||
||[http://git.sagemath.org/sage.git/commit/?id=aecbe5464d9002ecdcebf66cc78e639c3bc74f60
aecbe54]||{{{Cleanup of commented out code.}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/16451#comment:1>
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