Opened 6 years ago

Closed 2 years ago

#15484 closed enhancement (fixed)

Implement Yangian for gl(n)

Reported by: tscrim Owned by: sage-combinat
Priority: major Milestone: sage-8.0
Component: algebra Keywords: yangian, quantum groups
Cc: sage-combinat, aschilling, darij, bsalisbury1 Merged in:
Authors: Travis Scrimshaw Reviewers: Ben Salisbury
Report Upstream: N/A Work issues:
Branch: 8051da2 (Commits) Commit: 8051da25618f5275384196e7d5236386f7c06584
Dependencies: #23266, #23267, #23268, #23270 Stopgaps:

Description (last modified by tscrim)

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 6 years ago by tscrim

  • Branch changed from public/algebras/yangian to public/algebras/yangians
  • Commit set to 63f89cb187d7284792eee038cdcb0178c661a743
  • Status changed from new to needs_review

Last 10 new commits:

63f89cbAdded doctests to full coverage.
cd3e53eMerge branch 'public/monoids/15289-indexed' into u/tscrim/yangians
9dca526Added comparison operations.
a493beeMerge branch 'master' into public/monoids/15289-indexed
7e39c1fFixes for Yangian.
bc1b55cMerge branch 'public/monoids/15289-indexed' into u/tscrim/yangians
435a303Merge branch 'public/ticket/10963' of ssh://trac.sagemath.org:2222/sage into u/tscrim/yangians
80d55femerging sage/categories/category.py
b2064e6Merge branch 'u/tscrim/yangians' of ssh://trac.sagemath.org:2222/sage into u/tscrim/yangians
b113accMerge branch 'master' into u/tscrim/yangians

comment:2 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:3 Changed 5 years ago by git

  • Commit changed from 63f89cb187d7284792eee038cdcb0178c661a743 to 4fe436fc9684176c5eaca8b9063b354b27cc19f8

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

bd82ed8Merge branch 'develop' into public/monoids/15289-indexed
56703ebMade Indexed* have entry points through Free*.
163df6eChanged more _basis_keys to _indices, deprecated the former.
8db8e0aChanged _an_element_ to indexed_monoid.py.
760c939Merge branch 'public/monoids/15289-indexed' of trac.sagemath.org:sage into public/monoids/15289-indexed
03057a4Merge branch 'develop' into public/monoids/15289-indexed
a2996e0Merge branch 'develop' into public/monoids/15289-indexed
c1cc341Merge branch 'develop' into public/monoids/15289-indexed
c7baad9Merge branch 'public/monoids/15289-indexed' into public/algebras/yangians
4fe436fMerge branch 'public/algebras/yangians' of trac.sagemath.org:sage into public/algebras/yangians

comment:4 Changed 5 years ago by git

  • Commit changed from 4fe436fc9684176c5eaca8b9063b354b27cc19f8 to c467001c28656ac6ca798c954ea6bc05cf08a959

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

49068b2Merge branch 'develop' into public/monoids/15289-indexed
c467001Merge branch 'public/algebras/yangians' of trac.sagemath.org:sage into public/algebras/yangian

comment:5 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:6 Changed 5 years ago by git

  • Commit changed from c467001c28656ac6ca798c954ea6bc05cf08a959 to 0962d33d424449521c7f7c0b00b48b48e8228dce

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

0962d33Merge branch 'public/algebras/yangians' of trac.sagemath.org:sage into public/algebras/yangians

comment:7 Changed 5 years ago by git

  • Commit changed from 0962d33d424449521c7f7c0b00b48b48e8228dce to d5954ea12138d414b2246cd2ca06017d03bfe492

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

d5954eaFix from changes in #15289.

comment:8 Changed 5 years ago by git

  • Commit changed from d5954ea12138d414b2246cd2ca06017d03bfe492 to 629604f104592321a946c3b494b2284e7ff15364

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

6f98761Merge branch 'develop' into public/algebras/yangians
f8fe06cSome output tweaks.
629604fMany fixes for Yangians and added to the documentation.

comment:9 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:10 Changed 5 years ago by git

  • Commit changed from 629604f104592321a946c3b494b2284e7ff15364 to 36d07014aae9c6770b940e27bfdc5ee548f8cdb7

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

377d266Merge branch 'public/algebras/yangians' of trac.sagemath.org:sage into public/algebras/yangians
36d0701Added associated graded algebras to the Yangians.

comment:11 Changed 5 years ago by git

  • Commit changed from 36d07014aae9c6770b940e27bfdc5ee548f8cdb7 to 99a92e3fe4353507bbb650fd1dcf1cf6f82aa3a4

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

25c0fbclooked through clifford_algebra and filtered_algebras*; many TODOs left
2a62c3blift_* methods in algebras/clifford_algebra.py should remember the graded-filtered choice
15cf0dcfix and a first doctest for induced_graded_map
5029956another pitfall documented
292ef5fanother doctest
c2e84e1remaining doctests for induced_graded_map
03bd4cfpossibly controversial: graded_algebra and the three methods forming its interface are now cached_methods
8a747c0further edits
237daeaMerge branch 'public/categories/filtered_algebras-17096' of trac.sagemath.org:sage into public/algebras/yangians
99a92e3Added to catalog and refactored over #17096.

comment:12 Changed 5 years ago by tscrim

  • Dependencies changed from #10963 #15289 to #10963 #15289 #17096
  • Description modified (diff)

Refactored over #17096.

comment:13 Changed 4 years ago by git

  • Commit changed from 99a92e3fe4353507bbb650fd1dcf1cf6f82aa3a4 to 1770d3f50ac68932605fecbd0708d2a413d6f2f3

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

6051865add a doctest which hopefully works (hard to check while compiling)
570bc49Merge branch 'public/categories/super_categories-18044' into 6.9.b1
b91cd82trac #18044 correct one typo in the doc
7fd1df2Merge branch 'public/categories/super_categories-18044' of trac.sagemath.org:sage into public/categories/super_categories-18044
0579337Some reviewer tweaks and doc additions.
aec22ccAdded one more test.
4b2046fMerge branch 'public/categories/super_categories-18044' into public/categories/filtered_algebras-17096
3f67b6bFixing trivial doctest due to changes in category heirarchy.
fa476ddFixing double-colon in INPUT block.
1770d3fMerge branch 'public/algebras/yangians' of trac.sagemath.org:sage into public/algebras/yangians

comment:14 Changed 4 years ago by tscrim

  • Branch changed from public/algebras/yangians to public/algebras/yangians-15484
  • Commit changed from 1770d3f50ac68932605fecbd0708d2a413d6f2f3 to ea127f16470d0921d7b11272ad37c7c017e03a21
  • Dependencies #10963 #15289 #17096 deleted
  • Milestone changed from sage-6.4 to sage-6.11

New commits:

976c3a5imported patch yangians-ts.patch
446e08bFixes for Yangian.
6d21520Added doctests to full coverage.
b0c1bd1Fix from changes in #15289.
62acea7Some output tweaks.
03281d0Many fixes for Yangians and added to the documentation.
f5e13bcAdded associated graded algebras to the Yangians.
8ce5567Added to catalog and refactored over #17096.
ea127f1Fixing the Yangian due to recent changes in Sage.

comment:15 Changed 3 years ago by git

  • Commit changed from ea127f16470d0921d7b11272ad37c7c017e03a21 to 6b8bcd3f351d9abd7ffd86e7b307c952f356f5ad

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

6b8bcd3Merge branch 'public/algebras/yangians-15484' of trac.sagemath.org:sage into public/algebras/yangians-15484

comment:16 Changed 3 years ago by tscrim

  • Milestone changed from sage-7.0 to sage-7.2

comment:17 Changed 3 years ago by jdemeyer

  • Status changed from needs_review to needs_work

See patchbot (note that I don't personally care about this ticket, sorry)

comment:18 Changed 3 years ago by git

  • Commit changed from 6b8bcd3f351d9abd7ffd86e7b307c952f356f5ad to f297f3342642227be034b564356494a06c2863e0

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

236b896Merge branch 'public/algebras/yangians-15484' of trac.sagemath.org:sage into public/algebras/yangians-15484
f297f33Use sorting_key instead of generator_cmp.

comment:19 Changed 3 years ago by tscrim

  • Status changed from needs_work to needs_review

I understand; thanks for the heads-up.

comment:20 follow-up: Changed 3 years ago by tscrim

  • Cc andrew.mathas added
  • Milestone changed from sage-7.2 to sage-7.4

Just in case you're interested Andrew.

comment:21 in reply to: ↑ 20 Changed 3 years ago by andrew.mathas

  • Cc andrew.mathas removed

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 3 years ago by darij

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 3 years ago by git

  • Commit changed from f297f3342642227be034b564356494a06c2863e0 to ec4e344d7216c91d84aa5aae3c6342098d232d1d

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

ec4e344Added references.

comment:24 Changed 3 years ago by tscrim

Andrew, no problem.

Darij, I've added some references. A good reference is the MNO94 arXiv version.

comment:25 Changed 3 years ago by git

  • Commit changed from ec4e344d7216c91d84aa5aae3c6342098d232d1d to 8227771648f9603fb8f1fb66baa42fd74dae1bd7

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

8227771Merge branch 'public/algebras/yangians-15484' in 7.5.b6

comment:26 Changed 2 years ago by git

  • Commit changed from 8227771648f9603fb8f1fb66baa42fd74dae1bd7 to 5336becc00f10520678ef396676b8f50e2f283d3

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

9fbaa14Merge branch 'public/algebras/yangians-15484' of git://trac.sagemath.org/sage into public/algebras/yangians-15484
5336becMoving references.

comment:27 Changed 2 years ago by git

  • Commit changed from 5336becc00f10520678ef396676b8f50e2f283d3 to 8aa9ef9bde3adb3172b1234e27e384e9f786da09

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

a107debMerge branch 'develop' into t/15484/public/algebras/yangians-15484
8aa9ef9Added to documentation and fixed one doctest

comment:28 Changed 2 years ago by bsalisbury1

  • Cc bsalisbury1 added
  • Reviewers set to 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 2 years ago by bsalisbury1

  • Milestone changed from sage-7.4 to sage-8.0

comment:30 Changed 2 years ago by tscrim

Looks good. :)

comment:31 Changed 2 years ago by git

  • Commit changed from 8aa9ef9bde3adb3172b1234e27e384e9f786da09 to 9b977989bc1f2fb15852beb1780bb7d5e0c0da6a

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

9b97798More documentation additions

comment:32 follow-up: Changed 2 years ago by bsalisbury1

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 the counit_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 in reply to: ↑ 32 Changed 2 years ago by tscrim

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 the counit_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 2 years ago by git

  • Commit changed from 9b977989bc1f2fb15852beb1780bb7d5e0c0da6a to f26834b2c03f0565c0a97145b15002b22ff80ff2

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

e0f9c88Use monomial_coefficients instead of iteration for consistancy.
f61aae2Better mutliplication of PBW elements.
9cea97dMerge branch 'public/lie_algebras/pbw_mult_monomial_coeffs-23268' into public/algebras/yangians-15484
35aa493Added monomial_coefficients for gl.
eb19d0eMerge branch 'public/lie_algebras/monomial_gl-23267' into public/algebras/yangians-15484
a89bfccAdding an additional doctest checking U(gl_n) homomorphism.
5d87394Trivial doctest fixes.
707c5f1Merge branch 'public/linear_algebra/matrix_space_with_basis-22955' into public/algebras/yangians-15484
522d374Adding Filtered category to PBW basis.
f26834bMerge branch 'public/lie_algebras/pbw_filtered-23270' into public/algebras/yangians-15484

comment:35 Changed 2 years ago by tscrim

  • Dependencies set to #23266, #23267, #23268, #23270

I've updated the doc to be a more complete overview. I've also added a doctest that tests the homomorphism as filtered algebras with U(gln) (although this uncovered #23266, #23267, #23268, #23270).

comment:36 Changed 2 years ago by git

  • Commit changed from f26834b2c03f0565c0a97145b15002b22ff80ff2 to 5967289e2895e9be0b62af1ad5844e2c0d044c12

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

5967289Fixing typo antipode -> counit.

comment:37 Changed 2 years ago by git

  • Commit changed from 5967289e2895e9be0b62af1ad5844e2c0d044c12 to adb8d979e4deadb96749b87861cb3d0fea8370d7

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

adb8d97Fixed documentation errors

comment:38 Changed 2 years ago by git

  • Commit changed from adb8d979e4deadb96749b87861cb3d0fea8370d7 to 8051da25618f5275384196e7d5236386f7c06584

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

6393c5fFixed doctest errors
8051da2Merge branch 't/23267/public/lie_algebras/monomial_gl-23267' into t/15484/public/algebras/yangians-15484

comment:39 Changed 2 years ago by bsalisbury1

  • Status changed from needs_review to positive_review

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 2 years ago by vbraun

  • Branch changed from public/algebras/yangians-15484 to 8051da25618f5275384196e7d5236386f7c06584
  • Resolution set to fixed
  • Status changed from positive_review to closed
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