Implement the BZ multisegment crystal model

[tscrim]

For type A_n⁽¹⁾, we implement the BZ multisegment model for B(\infty)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​63f103c	Merge branch 'develop' into public/combinat/crystals/more_affine
​4d76623	Merge branch 'develop' into public/combinat/crystals/more_affine
​e9cfeff	Merge branch 'develop' into public/combinat/crystals/more_affine
​245aee2	Merge branch 'develop' into public/combinat/crystals/more_affine
​88c364b	Merge branch 'develop' into public/combinat/crystals/more_affine
​4160498	Merge branch 'develop' into public/combinat/crystals/more_affine
​060035a	Merge branch 'develop' into public/combinat/crystals/more_affine

[ncohen]

(must be adapted to #15882)

Nathann

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​c21494d	Merge branch 'public/combinat/crystals/more_affine' of trac.sagemath.org:sage into public/combinat/crystals/more_affine
​23c69db	Moved to the catalog.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​5cfd4e1	Cleaning up repr methods.
​0bf521f	Merge branch 'public/combinat/crystals/fix_repr-16172' into public/combinat/crystals/more_affine
​0ebd466	Fixed extraenous period.

[rws]

patchbot:

sage -t --long src/sage/combinat/rigged_configurations/kr_tableaux.py  # 1 doctest failed
sage -t --long src/sage/combinat/crystals/affinization.py  # 1 doctest failed
sage -t --long src/sage/schemes/plane_conics/con_rational_field.py  # Timed out
long time: 7 seconds ## line 148 ##

Suggest to set "long" for the last one.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​584c3e9	Merge branch 'public/combinat/crystals/more_affine' of trac.sagemath.org:sage into public/combinat/crystals/more_affine
​65bc2b0	Fixed != and doctests.

[tscrim]

This ticket has nothing to do with schemes and no bearing on that last doctest.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​255e43e

Merge branch 'public/combinat/crystals/more_affine' of trac.sagemath.org:sage into public/combint/crystals/more_affine

[jdemeyer]

Doesn't merge (note: I don't care about this ticket)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​dd5ef40

Merge branch 'public/combinat/crystals/more_affine' of trac.sagemath.org:sage into public/combinat/crystals/more_affine

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​9aca074	Merge branch 'public/combinat/crystals/more_affine' of trac.sagemath.org:sage into public/combinat/crystals/more_affine
​ca18c5c	Adding affinization crystal and fixing Kyoto path model weight.
​207520d	Merge branch 'public/crystals/kyoto_path_model_weight-18769' into public/combinat/crystals/more_affine

[bsalisbury1]

Hi Travis,

There are still some things that need to be changed with the multipartition model and the multisegment model. Some highlights:

• The Kleschev multipartition model and the JMMO multipartition model are closely related; perhaps both should be on the same ticket. Moreover, the display of these partitions should include the residues in cells of the partitions so that the charge of the partition is clear to the user (though maybe you have added this already after we talked a while back).

• There are two well-known crystal structures on multisegments, and they are related by the star-crystal operators. The convention being used should be clear and probably even the star-crystal operators should be added. In particular, see the 2009 paper by Jacon and Lecouvey in Pac. J. Math. It is my personal opinion that the notation and structure of that paper is the one that should be followed for the implementation, including changing the data structure of the multisegments to use dictionaries of the form {(interval) : coefficient}.

I vaguely remember there being some additional changes, too, but I can't be more specific until I have time to delve deeper into the patch.

Best, Ben

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​666be09

Merge branch 'public/combinat/crystals/more_affine' of trac.sagemath.org:sage into public/combinat/crystals/more_affine

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​ae76e72

Fix from bad merge.

[tscrim]

I have combined the Kleshchev partition crystal in with #20564.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​fef2f34

Merge branch 'public/combinat/crystals/more_affine' in 8.0.b2

[chapoton]

need to change the sort to use a sorting key

[tscrim]

Done. I also removed kleshchev.py as that is now done in #15508.

---

New commits:

​c241ef9

Removing Kleshchev crystal (now in #15508) and cmp.

[chapoton]

typo here:

Crystal of Bernstien-Zelevinsky

[chapoton]

otherwise, looks good. Once corrected, you can set to positive if a patchbot comes back green.

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​e1a5ac6	add combinat/module_list.rst to tracked files to merge develop branch
​b0d0fce	Merge branch 't/18769/public/crystals/kyoto_path_model_weight-18769' into t/15584/public/combinat/crystals/more_affine
​c49aa39	signature rule documentation added to multisegments
​b4be238	Affinization --> AffinizationOf in catalog.py
​14fd6a4	fixed merge error in combinat/module_list.rst
​ea900a7	doctests removed ... for now ...
​8fe08e9	Merge branch 'develop' into t/15584/public/combinat/crystals/more_affine
​18c1b20	Rebase
​7ed2949	merged with updates to description
​a368e5c	Merge branch 'public/combinat/crystals/more_affine' of git://trac.sagemath.org/sage into public/crystals/BZ_multisegments-15584

[tscrim]

Ben and I are doing a little bit more work on this right now.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​cc87885

Changing repr/latex formatting to use linear combinations.

[tscrim]

Ben, I've decided to keep the original data structure because it is easier to work with and less manipulations are needed to pass around the data (and maybe because I'm just lazy too). This is probably faster too because we don't have to sort on every crystal operator (and new objects should be relatively quick to sort because they started nearly sorted).

I've made a few small tweaks to Ben's expanded documentation, beyond changing the repr/latex to use linear combinations (this was the last big thing Ben wanted). So only my few changes left to check.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​aa69545

added negative sign to weight function on multisegments and extended the weight lattice for generalized young walls in highest_weight_crystals

[bsalisbury1]

The weight function was missing a negative sign and there was a doctest failure in highest_weight_crystals. Both are fixed now.

Thanks, Travis, for getting this finished!

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​071abec

removed B.S. from authorship, fixed date, and updated email

[tscrim]

Thank you both for doing the review.