#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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Changes (by nthiery):
* cc: sage-combinat (added)
Comment:
Replying to [comment:5 aschilling]:
> 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.
In a perfect world, a crystal of letter would have a method which
would take two letters a and b, and say whether b can be above a in a
column. There would be a default implementation (returning a<b in the
crystal of letters), and the type B crystal of letter would override
this default implementation appropriately.
If we are sure that no crystal of letter (or more generally crystal
that we want to use as letter in a tableau) will ever have a letter
called `0`, except for type `B`, or if we are willing to take the
risk, then I guess we can be lazy, and just leave things as they are.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8649#comment:6>
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