Opened 9 years ago
Closed 5 years ago
#15484 closed enhancement (fixed)
Implement Yangian for gl(n)
Reported by: | Travis Scrimshaw | Owned by: | Sage Combinat CC user |
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Priority: | major | Milestone: | sage-8.0 |
Component: | algebra | Keywords: | yangian, quantum groups |
Cc: | Sage Combinat CC user, Anne Schilling, Darij Grinberg, Ben Salisbury | Merged in: | |
Authors: | Travis Scrimshaw | Reviewers: | Ben Salisbury |
Report Upstream: | N/A | Work issues: | |
Branch: | 8051da2 (Commits, GitHub, GitLab) | Commit: | 8051da25618f5275384196e7d5236386f7c06584 |
Dependencies: | #23266, #23267, #23268, #23270 | Stopgaps: |
Description (last modified by )
Yangians can be seen as a deformation of U(gl[t]) and have many interesting connections to representation theory. See http://en.wikipedia.org/wiki/Yangian.
Change History (40)
comment:1 Changed 9 years ago by
Branch: | public/algebras/yangian → public/algebras/yangians |
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Commit: | → 63f89cb187d7284792eee038cdcb0178c661a743 |
Status: | new → needs_review |
comment:2 Changed 9 years ago by
Milestone: | sage-6.1 → sage-6.2 |
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comment:3 Changed 9 years ago by
Commit: | 63f89cb187d7284792eee038cdcb0178c661a743 → 4fe436fc9684176c5eaca8b9063b354b27cc19f8 |
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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
bd82ed8 | Merge branch 'develop' into public/monoids/15289-indexed
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56703eb | Made Indexed* have entry points through Free*.
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163df6e | Changed more _basis_keys to _indices, deprecated the former.
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8db8e0a | Changed _an_element_ to indexed_monoid.py.
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760c939 | Merge branch 'public/monoids/15289-indexed' of trac.sagemath.org:sage into public/monoids/15289-indexed
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03057a4 | Merge branch 'develop' into public/monoids/15289-indexed
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a2996e0 | Merge branch 'develop' into public/monoids/15289-indexed
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c1cc341 | Merge branch 'develop' into public/monoids/15289-indexed
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c7baad9 | Merge branch 'public/monoids/15289-indexed' into public/algebras/yangians
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4fe436f | Merge branch 'public/algebras/yangians' of trac.sagemath.org:sage into public/algebras/yangians
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comment:4 Changed 9 years ago by
Commit: | 4fe436fc9684176c5eaca8b9063b354b27cc19f8 → c467001c28656ac6ca798c954ea6bc05cf08a959 |
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comment:5 Changed 9 years ago by
Milestone: | sage-6.2 → sage-6.3 |
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comment:6 Changed 8 years ago by
Commit: | c467001c28656ac6ca798c954ea6bc05cf08a959 → 0962d33d424449521c7f7c0b00b48b48e8228dce |
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Branch pushed to git repo; I updated commit sha1. New commits:
0962d33 | Merge branch 'public/algebras/yangians' of trac.sagemath.org:sage into public/algebras/yangians
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comment:7 Changed 8 years ago by
Commit: | 0962d33d424449521c7f7c0b00b48b48e8228dce → d5954ea12138d414b2246cd2ca06017d03bfe492 |
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Branch pushed to git repo; I updated commit sha1. New commits:
d5954ea | Fix from changes in #15289.
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comment:8 Changed 8 years ago by
Commit: | d5954ea12138d414b2246cd2ca06017d03bfe492 → 629604f104592321a946c3b494b2284e7ff15364 |
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comment:9 Changed 8 years ago by
Milestone: | sage-6.3 → sage-6.4 |
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comment:10 Changed 8 years ago by
Commit: | 629604f104592321a946c3b494b2284e7ff15364 → 36d07014aae9c6770b940e27bfdc5ee548f8cdb7 |
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comment:11 Changed 8 years ago by
Commit: | 36d07014aae9c6770b940e27bfdc5ee548f8cdb7 → 99a92e3fe4353507bbb650fd1dcf1cf6f82aa3a4 |
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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
25c0fbc | looked through clifford_algebra and filtered_algebras*; many TODOs left
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2a62c3b | lift_* methods in algebras/clifford_algebra.py should remember the graded-filtered choice
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15cf0dc | fix and a first doctest for induced_graded_map
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5029956 | another pitfall documented
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292ef5f | another doctest
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c2e84e1 | remaining doctests for induced_graded_map
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03bd4cf | possibly controversial: graded_algebra and the three methods forming its interface are now cached_methods
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8a747c0 | further edits
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237daea | Merge branch 'public/categories/filtered_algebras-17096' of trac.sagemath.org:sage into public/algebras/yangians
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99a92e3 | Added to catalog and refactored over #17096.
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comment:12 Changed 8 years ago by
Dependencies: | #10963 #15289 → #10963 #15289 #17096 |
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Description: | modified (diff) |
Refactored over #17096.
comment:13 Changed 7 years ago by
Commit: | 99a92e3fe4353507bbb650fd1dcf1cf6f82aa3a4 → 1770d3f50ac68932605fecbd0708d2a413d6f2f3 |
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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
6051865 | add a doctest which hopefully works (hard to check while compiling)
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570bc49 | Merge branch 'public/categories/super_categories-18044' into 6.9.b1
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b91cd82 | trac #18044 correct one typo in the doc
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7fd1df2 | Merge branch 'public/categories/super_categories-18044' of trac.sagemath.org:sage into public/categories/super_categories-18044
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0579337 | Some reviewer tweaks and doc additions.
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aec22cc | Added one more test.
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4b2046f | Merge branch 'public/categories/super_categories-18044' into public/categories/filtered_algebras-17096
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3f67b6b | Fixing trivial doctest due to changes in category heirarchy.
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fa476dd | Fixing double-colon in INPUT block.
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1770d3f | Merge branch 'public/algebras/yangians' of trac.sagemath.org:sage into public/algebras/yangians
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comment:14 Changed 7 years ago by
Branch: | public/algebras/yangians → public/algebras/yangians-15484 |
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Commit: | 1770d3f50ac68932605fecbd0708d2a413d6f2f3 → ea127f16470d0921d7b11272ad37c7c017e03a21 |
Dependencies: | #10963 #15289 #17096 |
Milestone: | sage-6.4 → sage-6.11 |
New commits:
976c3a5 | imported patch yangians-ts.patch
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446e08b | Fixes for Yangian.
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6d21520 | Added doctests to full coverage.
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b0c1bd1 | Fix from changes in #15289.
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62acea7 | Some output tweaks.
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03281d0 | Many fixes for Yangians and added to the documentation.
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f5e13bc | Added associated graded algebras to the Yangians.
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8ce5567 | Added to catalog and refactored over #17096.
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ea127f1 | Fixing the Yangian due to recent changes in Sage.
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comment:15 Changed 7 years ago by
Commit: | ea127f16470d0921d7b11272ad37c7c017e03a21 → 6b8bcd3f351d9abd7ffd86e7b307c952f356f5ad |
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Branch pushed to git repo; I updated commit sha1. New commits:
6b8bcd3 | Merge branch 'public/algebras/yangians-15484' of trac.sagemath.org:sage into public/algebras/yangians-15484
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comment:16 Changed 7 years ago by
Milestone: | sage-7.0 → sage-7.2 |
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comment:17 Changed 6 years ago by
Status: | needs_review → needs_work |
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See patchbot (note that I don't personally care about this ticket, sorry)
comment:18 Changed 6 years ago by
Commit: | 6b8bcd3f351d9abd7ffd86e7b307c952f356f5ad → f297f3342642227be034b564356494a06c2863e0 |
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comment:19 Changed 6 years ago by
Status: | needs_work → needs_review |
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I understand; thanks for the heads-up.
comment:20 follow-up: 21 Changed 6 years ago by
Cc: | Andrew Mathas added |
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Milestone: | sage-7.2 → sage-7.4 |
Just in case you're interested Andrew.
comment:21 Changed 6 years ago by
Cc: | Andrew Mathas removed |
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Replying to tscrim:
Just in case you're interested Andrew.
Sorry Travis, but I don't play at all with Yangians and don't know much about them...
comment:22 Changed 6 years ago by
REFERENCES:: please!
I happen to be (slowly) reading my way through a paper on Capelli identities right now, and I'd be really interested in what seems to be the theory behind them, but I probably won't learn much from the code in itself :)
comment:23 Changed 6 years ago by
Commit: | f297f3342642227be034b564356494a06c2863e0 → ec4e344d7216c91d84aa5aae3c6342098d232d1d |
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Branch pushed to git repo; I updated commit sha1. New commits:
ec4e344 | Added references.
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comment:24 Changed 6 years ago by
Andrew, no problem.
Darij, I've added some references. A good reference is the MNO94 arXiv version.
comment:25 Changed 6 years ago by
Commit: | ec4e344d7216c91d84aa5aae3c6342098d232d1d → 8227771648f9603fb8f1fb66baa42fd74dae1bd7 |
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Branch pushed to git repo; I updated commit sha1. New commits:
8227771 | Merge branch 'public/algebras/yangians-15484' in 7.5.b6
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comment:26 Changed 6 years ago by
Commit: | 8227771648f9603fb8f1fb66baa42fd74dae1bd7 → 5336becc00f10520678ef396676b8f50e2f283d3 |
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comment:27 Changed 6 years ago by
Commit: | 5336becc00f10520678ef396676b8f50e2f283d3 → 8aa9ef9bde3adb3172b1234e27e384e9f786da09 |
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comment:28 Changed 6 years ago by
Cc: | Ben Salisbury added |
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Reviewers: | → Ben Salisbury |
Hi Travis,
I added some more to the documentation. Please make sure you are okay with it. I will continue the review soon.
Ben
comment:29 Changed 6 years ago by
Milestone: | sage-7.4 → sage-8.0 |
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comment:31 Changed 6 years ago by
Commit: | 8aa9ef9bde3adb3172b1234e27e384e9f786da09 → 9b977989bc1f2fb15852beb1780bb7d5e0c0da6a |
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Branch pushed to git repo; I updated commit sha1. New commits:
9b97798 | More documentation additions
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comment:32 follow-up: 33 Changed 6 years ago by
Hi Travis,
I'm still going through and adding more to the documentation, but some things (including some corrections) may be better completed by you. (I have the arXiv versions of Molev's references that you've listed, but I do not have a copy of the book you referenced.) For example:
- You've implemented the method
defining_polynomial
, but I cannot find that in my references. Moreover, in the references I do have, the notation you've used for the defining polynomial seems to be reserved for matrices whose entries are power series.
- I think there is an antipode method missing from the main
Yangian
class (and thecounit_on_basis
method, according to the documentation, returns the antipode).
- Add definitions for the coproduct, counit, and antipode. I added the coproduct definition already for the
Yangian
class.
- Can/should the Yang R-matrix also be added to this module?
comment:33 Changed 6 years ago by
Replying to bsalisbury1:
- You've implemented the method
defining_polynomial
, but I cannot find that in my references. Moreover, in the references I do have, the notation you've used for the defining polynomial seems to be reserved for matrices whose entries are power series.
This is the level \ell
version, so they become polynomials instead of power series.
- I think there is an antipode method missing from the main
Yangian
class (and thecounit_on_basis
method, according to the documentation, returns the antipode).
No, that is because I could not implement the antipode as it is defined in terms of an inverse matrix of power series. There is a ticket (I don't remember the number offhand) that gives a default implementation of the antipode in connected graded Hopf algebras.
In the counit_on_basis
, that is a typo from copy/pasting.
- Add definitions for the coproduct, counit, and antipode. I added the coproduct definition already for the
Yangian
class.
Let me know when you're done with your changed, and I can add them.
- Can/should the Yang R-matrix also be added to this module?
It would make for a good follow-up.
comment:34 Changed 5 years ago by
Commit: | 9b977989bc1f2fb15852beb1780bb7d5e0c0da6a → f26834b2c03f0565c0a97145b15002b22ff80ff2 |
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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
e0f9c88 | Use monomial_coefficients instead of iteration for consistancy.
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f61aae2 | Better mutliplication of PBW elements.
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9cea97d | Merge branch 'public/lie_algebras/pbw_mult_monomial_coeffs-23268' into public/algebras/yangians-15484
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35aa493 | Added monomial_coefficients for gl.
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eb19d0e | Merge branch 'public/lie_algebras/monomial_gl-23267' into public/algebras/yangians-15484
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a89bfcc | Adding an additional doctest checking U(gl_n) homomorphism.
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5d87394 | Trivial doctest fixes.
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707c5f1 | Merge branch 'public/linear_algebra/matrix_space_with_basis-22955' into public/algebras/yangians-15484
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522d374 | Adding Filtered category to PBW basis.
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f26834b | Merge branch 'public/lie_algebras/pbw_filtered-23270' into public/algebras/yangians-15484
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comment:35 Changed 5 years ago by
Dependencies: | → #23266, #23267, #23268, #23270 |
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comment:36 Changed 5 years ago by
Commit: | f26834b2c03f0565c0a97145b15002b22ff80ff2 → 5967289e2895e9be0b62af1ad5844e2c0d044c12 |
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Branch pushed to git repo; I updated commit sha1. New commits:
5967289 | Fixing typo antipode -> counit.
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comment:37 Changed 5 years ago by
Commit: | 5967289e2895e9be0b62af1ad5844e2c0d044c12 → adb8d979e4deadb96749b87861cb3d0fea8370d7 |
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Branch pushed to git repo; I updated commit sha1. New commits:
adb8d97 | Fixed documentation errors
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comment:38 Changed 5 years ago by
Commit: | adb8d979e4deadb96749b87861cb3d0fea8370d7 → 8051da25618f5275384196e7d5236386f7c06584 |
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comment:39 Changed 5 years ago by
Status: | needs_review → positive_review |
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Thanks for making those additions! I added some additional clarification and fixed some typos. In particular, now the PDF documentation will build. HTML documentation also builds and all tests pass.
comment:40 Changed 5 years ago by
Branch: | public/algebras/yangians-15484 → 8051da25618f5275384196e7d5236386f7c06584 |
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Resolution: | → fixed |
Status: | positive_review → closed |
Last 10 new commits: