Opened 9 years ago

Closed 8 years ago

#13838 closed enhancement (fixed)

Implementation of virtual Klebers algorithm

Reported by: tscrim Owned by: tscrim
Priority: major Milestone: sage-5.13
Component: combinatorics Keywords: rigged configurations
Cc: sage-combinat, aschilling Merged in: sage-5.13.beta0
Authors: Travis Scrimshaw Reviewers: Anne Schilling
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: #13871 #14469 Stopgaps:

Status badges

Description (last modified by tscrim)

The current implementation of KleberTree is only valid for the simply laced types. This ticket will implement the virtual Kleber algorithm and thus expand KleberTree to generate rigged configurations for all affine types.

Apply: trac_13838-virtual_kleber_alg-ts.patch

Attachments (2)

trac_13871-virtual_cartan_type-ts.patch (13.4 KB) - added by tscrim 9 years ago.
trac_13838-virtual_kleber_alg-ts.patch (59.2 KB) - added by tscrim 8 years ago.
New version

Download all attachments as: .zip

Change History (21)

comment:1 Changed 9 years ago by tscrim

  • Dependencies set to #13871

comment:2 Changed 9 years ago by tscrim

  • Cc sage-combinat added

comment:3 Changed 9 years ago by tscrim

  • Status changed from new to needs_review

Changed 9 years ago by tscrim

comment:4 Changed 9 years ago by tscrim

Since I attached the wrong patch...

For patchbot:

Apply only: trac_13838-virtual_kleber_alg-ts.patch

comment:5 Changed 8 years ago by tscrim

New version based over the changes in #13871.

For patchbot:

Apply: trac_13838-virtual_kleber_alg-ts.patch

comment:6 Changed 8 years ago by tscrim

Removed workaround of #14870 because it is now part of #13871.

For patchbot:

Apply: trac_13838-virtual_kleber_alg-ts.patch

comment:7 Changed 8 years ago by tscrim

  • Dependencies changed from #13871 to #13871 #14469

New version with (trivial) rebase over #14469.

For patchbot:

Apply: trac_13838-virtual_kleber_alg-ts.patch

comment:8 Changed 8 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:9 Changed 8 years ago by tscrim

New version over changes in #13871.

For patchbot:

Apply: trac_13838-virtual_kleber_alg-ts.patch

comment:10 Changed 8 years ago by chapoton

Hello,

  • there is a small typo "Kleber tree clases"
  • maybe you can use the :arxiv: role in the references ?

comment:11 follow-up: Changed 8 years ago by tscrim

With added arXiv role, fixed the typo, and bringing the doc up to new specs. Thanks for having a look at this Frederic.

For patchbot:

Apply: trac_13838-virtual_kleber_alg-ts.patch

comment:12 in reply to: ↑ 11 Changed 8 years ago by aschilling

Hi Travis,

It would be good if you could implement the tensor product multiplicity (and please call it tensor_product_multiplicity) which is formula (3.2) of http://arxiv.org/pdf/math/9809087.pdf in order to check that the code is giving the correct output. For nonsimply-laced types it would be the virtual analogue of this formula. The Kleber tree gives the admissible partitions, but to get the multiplicity one needs to sum over the product of binomial coefficients.

Also, I think it would be better to access the VirtualKleberTree? through its own class (rather than through KleberTree?). It is fine to inherit from KleberTree?, but the construction is mathematically inherently different. For example for type C_n^{(1)} the construction is via the A_{2n-1}^{(1)} Kleber tree and type A weights, rather than type C weights. Since this is mostly just used in later code on rigged configuration, I think it won't be necessary to export VirtualKleberTree? into the namespace.

Thanks for your work on this!

Anne

comment:13 follow-up: Changed 8 years ago by tscrim

Hey Anne,

Here's the new version with the changes we've discussed (via e-mail/in person) along with a method latex_options() for controlling the latex output. I also think it's okay for the virtual Kleber tree to accept simply-laced types as input and for them to not compare as equal (since they are different mathematical constructions because we consider it as a folded type). I've documented this behavior.

Thank you for doing the review,
Travis

For patchbot:

Apply: trac_13838-virtual_kleber_alg-ts.patch

comment:14 in reply to: ↑ 13 Changed 8 years ago by aschilling

Hi Travis,

If you want to allow for simply-laced input in the VirtualKleberTree?, don't you want to select all nodes and bracket them in the output? Otherwise the behavior is different from the simply-laced and non-simply-laced types. If it is really just the same as the usual KleberTree?, then why not make them equal in this case?

Best,

Anne

Changed 8 years ago by tscrim

New version

comment:15 follow-up: Changed 8 years ago by tscrim

  • Description modified (diff)

Hey Anne,

I made it raise an error on simply-laced types.

Best,
Travis

For patchbot:

Apply: trac_13838-virtual_kleber_alg-ts.patch

comment:16 in reply to: ↑ 15 Changed 8 years ago by aschilling

Hi Travis,

Looks good now (you want to add a test for the simply-laced types in the VirtualKleberTree? for completeness).

Anne

comment:17 Changed 8 years ago by aschilling

  • Keywords rigged configurations added
  • Reviewers set to Anne Schilling
  • Status changed from needs_review to positive_review

comment:18 Changed 8 years ago by jdemeyer

  • Milestone changed from sage-5.12 to sage-5.13

comment:19 Changed 8 years ago by jdemeyer

  • Merged in set to sage-5.13.beta0
  • Resolution set to fixed
  • Status changed from positive_review to closed
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