Add methods to rigged configurations #15560

tscrim · 2013-12-21T06:51:25Z

Adds some extra methods to rigged configurations: the action of the left column splitting and the basic operation in the bijection with tensor product of KR tableaux.

Depends on #13872
Depends on #15882

CC: @sagetrac-sage-combinat @anneschilling

Component: combinatorics

Keywords: rigged configurations

Author: Travis Scrimshaw

Branch/Commit: 1e15993

Reviewer: Anne Schilling

Issue created by migration from https://trac.sagemath.org/ticket/15560

The text was updated successfully, but these errors were encountered:

tscrim · 2013-12-21T06:51:45Z

Branch: public/combinat/rigged_configurations/methods-15560

sagetrac-git · 2013-12-21T06:52:10Z

Commit: 365b520

sagetrac-git · 2013-12-21T06:52:10Z

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

`365b520`	`Added methods to RC's.`
`c1cda2b`	`Merge branch 'public/combinat/rigged_configurations/bijections-13872' into public/combinat/rigged_configurations/improvements`
`85b6446`	`Reorded all.py to match original (so fewer changes).`
`a51b39f`	`Fixed minor typo in cobminat/crystals/letters.pyx.`
`17a04d7`	`Added deprecatd classes back with warnings.`
`538c594`	`Merge branch 'master' into public/combinat/rigged_configurations/bijections-13872`
`29c9d34`	`[FIXUP] 5.13.beta5: update git specific files`
`0aa3fed`	`5.13.beta5`
`8f2b136`	`5.13.beta5`
`42bc8b6`	`some edits to docs`

sagetrac-git · 2013-12-22T20:40:09Z

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

`0050d2e`	`Forbade spinor cases.`
`21bf27f`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`

sagetrac-git · 2013-12-22T20:40:09Z

Changed commit from 365b520 to 0050d2e

sagetrac-git · 2014-03-14T15:01:54Z

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

`8bac0b2`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`e17c7c8`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`fd8b9c0`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`c7c399e`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`d9a96c2`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`3ccd75d`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`bf56c7f`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`bb910cc`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`

sagetrac-git · 2014-03-14T15:01:54Z

Changed commit from 0050d2e to bb910cc

sagetrac-git · 2014-03-18T15:48:33Z

Changed commit from bb910cc to 4695e88

sagetrac-git · 2014-03-18T15:48:33Z

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

`4695e88`	`Implemented changes Anne and I discussed.`

tscrim · 2014-03-21T00:21:18Z

comment:8

Thanks in advance for doing the review.

anneschilling · 2014-03-21T04:19:10Z

comment:9

Hi Travis,

Here are further comments:

+ If we are construction a rigged configuration from a rigged configuration
+ (say of another type) and we don't want to recompute the vacancy numbers,
+ we can use the ``use_vacancy_numbers`` to avoid the recomputation.

This is not a sentence. Perhaps you want "If we are constructing"?

Also, it would be great to add left_split as a method to KirillovReshetikhinTableaux and possibly also the right_split method! This can be just done by using the bijection to rigged configurations, but it would be very handy to have these methods directly on KirillovReshetikhinTableaux as well.

Thanks,

Anne

sagetrac-git · 2014-03-23T19:24:17Z

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

`78489a6`	`trac #15882: review (typos)`
`968f9f6`	`Fixing broken links and other misc cleanup.`
`faa5507`	`Fixed failing doctests.`
`207f38e`	`Fixed last doc errors.`
`007043b`	`Fixed failing doctests and some cleanup of classical_crystals.`
`6314a36`	`Fixed doc of classical_crystals and added regular_crystals to doc.`
`ac1dcd5`	`Merge branch 'public/combinat/crystals/catalog-15882' into public/combinat/rigged_configurations/methods-15560`
`2cc751e`	`Fixed doctest failures in rigged_configurations folder.`
`3be2a08`	`Merge branch 'public/combinat/crystals/catalog-15882' into public/combinat/rigged_configurations/methods-15560`
`df3a9eb`	`Some doctest fixes.`

sagetrac-git · 2014-03-23T19:24:17Z

Changed commit from 4695e88 to df3a9eb

tscrim · 2014-03-23T19:31:41Z

Changed dependencies from #13872 to #13872 #15882

tscrim · 2014-03-23T19:31:41Z

Reviewer: Anne Schilling

tscrim · 2014-03-23T19:31:41Z

comment:12

Here's the major changes:

Based this off Implement a catalog for crystals #15882.
Added the Luzstig involution to (tensor products of) KR tableaux, KR crystals, and rigged configurations.
Added left/right splitting maps to (tensor products of) KR tableaux and rigged configurations. (The right splitting map is non-trivial on KR tableaux; look in type D₄⁽¹⁾ at the B^2,2 module generators.)
Moved opposition_automorphism() from the crystals category into Cartan types.
Fixed the typo noted above.

Best,

Travis

sagetrac-git · 2014-03-24T14:56:34Z

Changed commit from df3a9eb to e7e2ad5

sagetrac-git · 2014-03-24T14:56:34Z

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

`b2b3fa6`	`Merge branch 'develop' into public/combinat/crystals/catalog-15882`
`e7e2ad5`	`Merge branch 'public/combinat/crystals/catalog-15882' into public/combinat/rigged_configurations/methods-15560`

sagetrac-git · 2014-06-11T01:26:45Z

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

`b5b442f`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`43da3ef`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`c821bde`	`Initial graph viewing. Only for type D and types w/o special run() methods.`
`8d173ee`	`Merge branch 'develop' into u/tscrim/rc_bij_pdf`
`e8011bd`	`Changed input method and added constructions to other types.`
`54f1a4a`	`Merge branch 'develop' into u/tscrim/rc_bij_pdf`
`e103d1e`	`Merge branch 'u/tscrim/rc_bij_pdf' into public/combinat/rigged_configurations/methods-15560`

anneschilling · 2014-07-19T22:03:08Z

comment:22

Hi Travis,

Here are some more comments:

The documentation of right_split has a ` missing. Please run the documentation to see that it actually compiles!
Please add the map \theta to rigged configuration and compare to lusztig_involution.
Please add tests and more explanations what build_graph does. Explain which graph it is computing. Also the following fails:

sage: RC = RiggedConfigurations(['D', 4, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import RCToKRTBijectionTypeD
sage: RCToKRTBijectionTypeD(RC(partition_list=[[1],[1],[1],[1]])).run()
[[2], [-3]]

sage: RCToKRTBijectionTypeD(RC(partition_list=[[1],[1],[1],[1]])).run(build_graph=True)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-10-1c82ae944c4d> in <module>()
----> 1 RCToKRTBijectionTypeD(RC(partition_list=[[Integer(1)],[Integer(1)],[Integer(1)],[Integer(1)]])).run(build_graph=True)

/Applications/sage/local/lib/python2.7/site-packages/sage/combinat/rigged_configurations/bij_type_D.pyc in run(self, verbose, build_graph)
    513 
    514                     if build_graph:
--> 515                         y = self.rigged_con.parent()(*[x._clone() for x in self.cur_partitions])
    516                         self._graph.append([self._graph[-1][1], (y, len(self._graph)), letters(b)])
    517 

/Applications/sage/local/lib/python2.7/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:8924)()

/Applications/sage/local/lib/python2.7/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args (sage/structure/coerce_maps.c:4637)()

/Applications/sage/local/lib/python2.7/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args (sage/structure/coerce_maps.c:4501)()

/Applications/sage/local/lib/python2.7/site-packages/sage/combinat/rigged_configurations/rigged_configurations.pyc in _element_constructor_(self, *lst, **options)
    717             lst = lst[0]
    718 
--> 719         return self.element_class(self, list(lst), **options)
    720 
    721     def _calc_vacancy_number(self, partitions, a, i, **options):

/Applications/sage/local/lib/python2.7/site-packages/sage/combinat/rigged_configurations/rigged_configuration_element.pyc in __init__(self, parent, rigged_partitions, **options)
    289             nu[-1] = RiggedPartitionTypeB(nu[-1])
    290 
--> 291         ClonableArray.__init__(self, parent, nu)
    292 
    293     def _repr_(self):

/Applications/sage/local/lib/python2.7/site-packages/sage/structure/list_clone.so in sage.structure.list_clone.ClonableArray.__init__ (sage/structure/list_clone.c:3758)()

/Applications/sage/local/lib/python2.7/site-packages/sage/structure/list_clone.so in sage.structure.list_clone.ClonableArray.check (sage/structure/list_clone.c:5758)()

/Applications/sage/local/lib/python2.7/site-packages/sage/combinat/rigged_configurations/rigged_configuration_element.pyc in check(self)
    492             for i, vac_num in enumerate(partition.vacancy_numbers):
    493                 if vac_num < partition.rigging[i]:
--> 494                     raise ValueError("rigging can be at most the vacancy number")
    495 
    496     def to_tensor_product_of_kirillov_reshetikhin_tableaux(self, display_steps=False, build_graph=False):

ValueError: rigging can be at most the vacancy number

Anne

sagetrac-git · 2014-07-20T17:47:02Z

Changed commit from e103d1e to 2874083

sagetrac-git · 2014-07-20T17:47:02Z

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

`c612e7f`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`40c98dc`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`56119bf`	`Added theta map, fixed bugs and expanded doc.`
`2874083`	`Minor rewording of build_graph param in bijections.`

tscrim · 2014-07-20T17:53:06Z

comment:24

Replying to @anneschilling:

The documentation of right_split has a ` missing. Please run the documentation to see that it actually compiles!

I couldn't find this and the documentation built without an issue and looks okay to me (although there was a missing 'u').

Please add the map \theta to rigged configuration and compare to lusztig_involution.

Added under the name complement. In general, it will be different than lusztig_involution, which fixes each classical component, whereas \theta fixes the classical structure but permutes the classical components. Or did you mean you wanted me to add a doctest showing this?

Please add tests and more explanations what build_graph does. Explain which graph it is computing. Also the following fails:

This was due to before, the element constructor always preserved the vacancy numbers and now it recomputes it unless explicitly stated. Fixed with added tests. I expanded the documentation in to_tensor_..._tableaux() as well.

anneschilling · 2014-07-21T15:15:23Z

comment:25

Replying to @tscrim:

Replying to @anneschilling:

The documentation of right_split has a ` missing. Please run the documentation to see that it actually compiles!

I couldn't find this and the documentation built without an issue and looks okay to me (although there was a missing 'u').

There is a ` missing in

+ Let `\ast` denote the :meth:`Lusztig involution<lusztig_involution>`,
+ and `\mathrm{ls}` as the :meth:`left splitting map<left_split>`.
+ The right splitting map is defined as
+ \mathrm{rs} := \ast \circ \mathrm{ls} \circ \ast`.

Please add the map \theta to rigged configuration and compare to lusztig_involution.

Added under the name complement. In general, it will be different than lusztig_involution, which fixes each classical component, whereas \theta fixes the classical structure but permutes the classical components. Or did you mean you wanted me to add a doctest showing this?

Under \bar \Phi the map \star (which I guess is what you call lusztig_involution) intertwines with \theta. It would be good to add a check like that.

Please add tests and more explanations what build_graph does. Explain which graph it is computing. Also the following fails:

This was due to before, the element constructor always preserved the vacancy numbers and now it recomputes it unless explicitly stated. Fixed with added tests. I expanded the documentation in to_tensor_..._tableaux() as well.

Even though it is stated in the documentation, that build_graph is an optional
parameter, it does not seem to take this input:

sage: rc = RC(partition_list=[[1],[1],[1],[1]])
sage: rc.to_tensor_product_of_kirillov_reshetikhin_crystals(build_graph=True)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-8-702cb808a701> in <module>()
----> 1 rc.to_tensor_product_of_kirillov_reshetikhin_crystals(build_graph=True)

TypeError: to_tensor_product_of_kirillov_reshetikhin_crystals() got an unexpected keyword argument 'build_graph'

What is the difference between build_graph and display_steps?

Anne

sagetrac-git · 2014-07-21T16:45:37Z

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

`6552c61`	`Fixed doc, added intertwining doctest, and added build_graph to to_*_crystals.`

sagetrac-git · 2014-07-21T16:45:37Z

Changed commit from 2874083 to 6552c61

sagetrac-git · 2014-07-21T16:56:31Z

Changed commit from 6552c61 to a985081

sagetrac-git · 2014-07-21T16:56:31Z

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

`a985081`	`Tweaked wording of param display_steps doc.`

tscrim · 2014-07-21T16:57:48Z

comment:28

Replying to @anneschilling:

There is a ` missing in
...

Ah, I forgot about the right split for KR tableaux. :P Fixed.

Under \bar \Phi the map \star (which I guess is what you call lusztig_involution) intertwines with \theta. It would be good to add a check like that.

I've added a doctest.

Even though it is stated in the documentation, that build_graph is an optional
parameter, it does not seem to take this input:

sage: rc = RC(partition_list=[[1],[1],[1],[1]])
sage: rc.to_tensor_product_of_kirillov_reshetikhin_crystals(build_graph=True)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-8-702cb808a701> in <module>()
----> 1 rc.to_tensor_product_of_kirillov_reshetikhin_crystals(build_graph=True)

TypeError: to_tensor_product_of_kirillov_reshetikhin_crystals() got an unexpected keyword argument 'build_graph'

This is because this was not a parameter in to_tensor_product_of_kirillov_reshetikhin_crystals, but in *_tableaux. I've also added the parameter (and doc/test) to the 'to TP of KR crystals' methods.

What is the difference between build_graph and display_steps?

The first one constructs and returns the graph, the latter outputs each step to the terminal. I've changed output to print to avoid some ambiguity.

anneschilling · 2014-07-22T04:35:44Z

comment:29

Why is the right_split that you implemented the correct map? I thought that rs = * ls * using the * map.

tscrim · 2014-07-22T18:55:54Z

comment:30

Replying to @anneschilling:

Why is the right_split that you implemented the correct map? I thought that rs = * ls * using the * map.

right_split is implemented as * ls * (where * is the Lusztig involution) for both rigged configurations and KR tableaux.

anneschilling · 2014-07-23T01:08:16Z

comment:31

With your current code

sage: RC = RiggedConfigurations(['D', 4, 1], [[2,2],[2, 2]])
sage: all((rc.right_split()).to_tensor_product_of_kirillov_reshetikhin_tableaux() == (rc.to_tensor_product_of_kirillov_reshetikhin_tableaux()).right_split() for rc in RC)
False

I think you need to use complement in the definition the RC side. Also, it might be better to rename complement to complement_rigging for a more descriptive name.

sagetrac-git · 2014-07-23T02:19:13Z

Changed commit from a985081 to 51c8ba2

sagetrac-git · 2014-07-23T02:19:13Z

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

`dc3202e`	`Merge branch 'develop' into public/combinat/rigged_configurations/methods-15560`
`51c8ba2`	`Changed complement -> complement_rigging and fixed right_split on RC side.`

sagetrac-git · 2014-07-23T02:55:19Z

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

`013737b`	`Added right_box method for symmetry.`

sagetrac-git · 2014-07-23T02:55:19Z

Changed commit from 51c8ba2 to 013737b

anneschilling · 2014-07-23T21:30:10Z

comment:34

Hi Travis,

Thanks for the changes. I get the following failure when trying to play with the code

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D',4,1], [[2,2], [1,2]])
sage: all(b.to_rigged_configuration().lusztig_involution() == b.lusztig_involution().to_rigged_configuration() for b in KRT)
False

Anne

sagetrac-git · 2014-07-26T15:40:10Z

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

`1e15993`	`Removed lusztig_involution and right_box.`

sagetrac-git · 2014-07-26T15:40:10Z

Changed commit from 013737b to 1e15993

tscrim · 2014-07-26T15:41:18Z

comment:36

Hey Anne,

I've removed the lusztig_involution() and right_box() methods for rigged configurations as per our discussion.

anneschilling · 2014-07-27T01:41:00Z

comment:37

Ok, looks good now!

Anne

vbraun · 2014-07-27T04:41:18Z

Changed branch from public/combinat/rigged_configurations/methods-15560 to 1e15993

tscrim added this to the sage-6.1 milestone Dec 21, 2013

tscrim added c: combinatorics labels Dec 21, 2013

tscrim assigned sagetrac-sage-combinat Dec 21, 2013

tscrim added the s: needs review label Dec 21, 2013

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.1, sage-6.2 Jan 30, 2014

anneschilling added s: needs work and removed s: needs review labels Mar 21, 2014

tscrim added s: needs review and removed s: needs work labels Mar 23, 2014

anneschilling added s: positive review and removed s: needs review labels Jul 27, 2014

vbraun removed the s: positive review label Jul 27, 2014

vbraun closed this as completed in 3f1c124 Jul 27, 2014

tscrim mentioned this issue Mar 23, 2016

Implement crystal of rigged configurations #16324

Closed

fchapoton mentioned this issue Dec 28, 2018

remove various old deprecated stuff #26866

Closed

Add methods to rigged configurations #15560

Add methods to rigged configurations #15560

Comments

tscrim commented Dec 21, 2013

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