#8649: to_tableau method broken for crystals of type B
------------------------------+---------------------------------------------
Reporter: aschilling | Owner: sage-combinat
Type: defect | Status: positive_review
Priority: major | Milestone: sage-4.4
Component: combinatorics | Keywords: crystals
Author: Anne Schilling | Upstream: N/A
Reviewer: Dan Bump | Merged:
Work_issues: |
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Comment(by aschilling):
Dear Dan and Nicolas,
Thank you for the review. The mathematical reason why in type B the 0 is
special,
is that it sits in a string of length 2:
1 -> 2 -> 0 -> -2 -> -1
Hence a column of height 2 for example can become
2 0 0 0
1 -2-> 1 -1-> 2 -2-> 0
since in the tensor product always the rightmost unbracketed element is
changed.
For similar reasons, in the row case there cannot be two 0s.
So this is really due to the string of length 2 which the other crystal of
letters
do not have. Nicolas, how else should the code be written to detect this?
The paper by Kashiwara-Nakashima on tableaux for other types is also
pretty
case specific.
Best wishes,
Anne
Replying to [comment:4 bump]:
> I wrote:
>
> > My conclusion is that the patch is correct and fixes a bad book. It
should be merged.
>
> I meant a bad *bug*.
>
> Replying to Nicolas:
>
> It was news to me that Type B tableaux (which were first invented I
think by Kashiwara) do not have to be column strict when 0 is involved.
That is, Type A tableaux are the classical ones and every column is
strict. It looks to me as if there actually is something different about
0.
> I don't understand this as a mathematical point, but I did enough
testing that I am sure
> the patch is right.
>
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8649#comment:5>
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