Opened 6 years ago
Closed 6 years ago
#14252 closed enhancement (fixed)
Implementation of quantum LS paths
Reported by: | aschilling | Owned by: | sage-combinat |
---|---|---|---|
Priority: | major | Milestone: | sage-5.10 |
Component: | combinatorics | Keywords: | crystals, KR crystals |
Cc: | sage-combinat | Merged in: | sage-5.10.beta0 |
Authors: | Anne Schilling | Reviewers: | Mark Shimozono, Travis Scrimshaw |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #14192 | Stopgaps: |
Description (last modified by )
This patch cleans up the interface of CrystalOfLSPaths. In particular, the input is now a weight, whereas before it took a cartan type and a list of coefficients. The class call function still allows this input format.
In addition, a new implementation of one-column Kirillov-Reshetikhin crystals is given in terms of level-zero CrystalOfLSPaths together with the energy function and one-dimensional configuration sum.
Attachments (1)
Change History (22)
comment:1 Changed 6 years ago by
- Component changed from PLEASE CHANGE to combinatorics
- Owner changed from tbd to sage-combinat
comment:2 Changed 6 years ago by
- Description modified (diff)
comment:3 Changed 6 years ago by
- Status changed from new to needs_review
comment:4 follow-up: ↓ 5 Changed 6 years ago by
comment:5 in reply to: ↑ 4 ; follow-up: ↓ 7 Changed 6 years ago by
Hi Mark,
Thanks for the comments! The CrystalOfProjectedLevelZeroLSPaths are now implemented and I added tests to compare with tensor products of KR crystals. The energy functions are still missing (but can be added).
Anne
comment:6 Changed 6 years ago by
- Description modified (diff)
comment:7 in reply to: ↑ 5 Changed 6 years ago by
Hi Mark,
The energy function and one-dimensional configuration sums are now implemented. Could you please review the patch?
Thanks,
Anne
comment:8 follow-up: ↓ 9 Changed 6 years ago by
- Dependencies set to #14192
comment:9 in reply to: ↑ 8 ; follow-up: ↓ 10 Changed 6 years ago by
Hi Travis,
I made the changes we discussed by e-mail.
Anne
comment:10 in reply to: ↑ 9 Changed 6 years ago by
Added a sanity check for the user input!
Anne
comment:11 follow-up: ↓ 13 Changed 6 years ago by
Three more small things:
- On lines 50-52 of
littelmann_paths.py
, the extra lines to the inputs list need to be de-indented by 2 spaces (to line up with the first non-whitespace character of the item). - On line 813, could you use the (relatively new) arXiv linking:
:arXiv:`1211.6019`
- Should
KirillovReshetikhinCrystalFromLSPaths
be imported into the global namespace?
Other than those things, this is a positive review.
Best,
Travis
comment:12 Changed 6 years ago by
- Reviewers changed from Mark Shimozono to Mark Shimozono, Travis Scrimshaw
comment:13 in reply to: ↑ 11 Changed 6 years ago by
Three more small things:
- On lines 50-52 of
littelmann_paths.py
, the extra lines to the inputs list need to be de-indented by 2 spaces (to line up with the first non-whitespace character of the item).
Done.
- On line 813, could you use the (relatively new) arXiv linking:
:arXiv:`1211.6019`
Done. I also changed the two things requested by e-mail.
- Should
KirillovReshetikhinCrystalFromLSPaths
be imported into the global namespace?
Since the eventual aim is to link to this class from KirillovReshetikhinCrystal? itself, I think it is better to leave it as is and not import this into the namespace for right now.
Anne
comment:14 follow-up: ↓ 15 Changed 6 years ago by
- Status changed from needs_review to positive_review
Okay. Looks good to me now. Thank you.
Travis
comment:15 in reply to: ↑ 14 Changed 6 years ago by
Thanks Travis!
comment:16 Changed 6 years ago by
- Milestone changed from sage-5.9 to sage-5.10
comment:17 follow-up: ↓ 18 Changed 6 years ago by
- Status changed from positive_review to needs_work
sage -t devel/sage/sage/categories/weyl_groups.py ********************************************************************** File "devel/sage/sage/categories/weyl_groups.py", line 118, in sage.categories.weyl_groups.WeylGroups.ParentMethods.quantum_bruhat_graph Failed example: g = W.quantum_bruhat_graph([1,3]) Exception raised: Traceback (most recent call last): File "/mazur/release/merger/sage-5.10.beta0/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 466, in _run self.execute(example, compiled, test.globs) File "/mazur/release/merger/sage-5.10.beta0/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 825, in execute exec compiled in globs File "<doctest sage.categories.weyl_groups.WeylGroups.ParentMethods.quantum_bruhat_graph[1]>", line 1, in <module> g = W.quantum_bruhat_graph([Integer(1),Integer(3)]) File "cachefunc.pyx", line 1460, in sage.misc.cachefunc.CachedMethodCaller.__call__ (sage/misc/cachefunc.c:7292) TypeError: unhashable type: 'list' **********************************************************************
Changed 6 years ago by
comment:18 in reply to: ↑ 17 Changed 6 years ago by
Fixed the failing doctests. The quantum Bruhat graph now takes a tuple as input.
Anne
comment:19 Changed 6 years ago by
- Status changed from needs_work to needs_review
comment:20 Changed 6 years ago by
- Status changed from needs_review to positive_review
Changes also look good to me as well.
comment:21 Changed 6 years ago by
- Merged in set to sage-5.10.beta0
- Resolution set to fixed
- Status changed from positive_review to closed
I propose the implementation of the crystal class
CrystalOfProjectedLevelZeroLSPaths
that takes as input an affine Cartan type and an element of its finite weight space. The result should be paths in the finite weight space, together with a function that can recover the head and tail energy. These crystals should know that they are finite as well.
KirillovReshetikhinCrystalFromLSPaths can be an instance of it.
One could doctest CrystalOfProjectedLevelZeroLSPaths by isomorphism with tensor products of its single-column versions.
Another interesting function would be to write the Naito-Sagaki lift from KirillovReshetikhinCrystalFromLSPaths to the level zero LS paths living in the level zero affine weight lattice (with the null root). Perhaps that is the way the energy function should be implemented.