Add tensor_factors() method to TensorProductOfHighestWeightModules in quantum_group_gap
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This fails with gap_packages installed since #34393.
However, there is another failure for the submodules. I do not think subobjects of tensor products should have a tensor product structure.
CC: @mkoeppe @fchapoton
Component: algebra
Keywords: quantum group, representation
Author: Travis Scrimshaw
Branch/Commit: 918c372
Reviewer: Matthias Koeppe
Issue created by migration from https://trac.sagemath.org/ticket/34635
Replying to [ticket:34635 Travis Scrimshaw]:
I do not think subobjects of tensor products should have a tensor product structure.
I disagree
But it should be documented
If I take V (x) W and the submodule V (x) w for some fixed w \in W, what is the tensor product structure on that? I don't see how to make sense of that.
What are the morphisms in the category of tensor products of modules?
There is no difference with modules. Are you trying to say that we should have the tensor factors of V (x) w be V and the span of w? That might work, but how would this work with the problem at hand, where we have an A-repr inside of V (x) W?
Replying to Travis Scrimshaw:
There is no difference with modules.
Let me elaborate slightly on this. I believe we agree that the tensor product of finite dimensional modules is equivalent to the category of modules (over a (commutative?) ring R). It just has a little extra information about how the module was constructed (which is important for things like graded modules and representations).
Anyhow, an optional package gap_packages ought to pass the doctests, and it does not at the moment. Can you at least silence these warnings?
Author: Travis Scrimshaw
Here is a version where I work around the submodules of tensor products thinking it is a tensor product: I weakened the category of the submodules.
New commits:
67340e2 | Adding tensor_factors() to tensor product of quantum group modules. |
918c372 | Changing the category of the submodule to get around subobjects of tensor products being in tensor products. |
LGTM. Tests OK with gap_packages installed.
Reviewer: Matthias Koeppe
Changed branch from public/algebra/tensor_quantum_group-34635 to 918c372