#14573: Implement path realization for affine crystals
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.11
Component: combinatorics | Resolution:
Keywords: affine crystals, days49 | Work issues:
Report Upstream: N/A | Reviewers: Ben Salisbury,
Anne Schilling
Authors: Travis Scrimshaw | Merged in:
Dependencies: #14402 | Stopgaps:
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Comment (by aschilling):
Hi Travis,
I have some further comments:
- The commit message is the merge of two patches; you might want to edit
it!
- There is a typo "canonial" -> canonical
- Please explain what you mean by the bar on the weights. Also it would be
a good idea to mention that `\Lambda_i` are the fundamental weights.
- Please mention that you are using the anti-Kashiwara convention for
tensor factors (since I think your documentation differs in this from some
of the literature and this might be confusing to users).
- Perhaps use capital `N` also in the equation before the sentence "We
note by Lemma 10.6.2 in [HK02] ....".
- The documentation says B is a list of perfect crystals. But as far as I
can see, in the examples the input is a single crystal. Could you please
clarify? As I told Travis at some point in person, I think it would be a
good idea to allow a list of crystals of the same level. If
[B1,B2,....,Bk] would be such a list, one would use `\cdots \otimes B_1
\otimes B_2 \otimes \cdots B_k \otimes B_1 \otimes \cdots B_k \otimes
B(\lambda)` as the model for the affine highest weight crystal.
- Could you add the affine grading? This would be useful since it is equal
to the energy function!
Thank you,
Anne
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14573#comment:8>
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