Opened 8 years ago
Closed 5 years ago
#15484 closed enhancement (fixed)
Implement Yangian for gl(n)
Reported by:  tscrim  Owned by:  sagecombinat 

Priority:  major  Milestone:  sage8.0 
Component:  algebra  Keywords:  yangian, quantum groups 
Cc:  sagecombinat, aschilling, darij, bsalisbury1  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 8 years ago by
 Branch changed from public/algebras/yangian to public/algebras/yangians
 Commit set to 63f89cb187d7284792eee038cdcb0178c661a743
 Status changed from new to needs_review
comment:2 Changed 8 years ago by
 Milestone changed from sage6.1 to sage6.2
comment:3 Changed 8 years ago by
 Commit changed from 63f89cb187d7284792eee038cdcb0178c661a743 to 4fe436fc9684176c5eaca8b9063b354b27cc19f8
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
bd82ed8  Merge branch 'develop' into public/monoids/15289indexed

56703eb  Made Indexed* have entry points through Free*.

163df6e  Changed more _basis_keys to _indices, deprecated the former.

8db8e0a  Changed _an_element_ to indexed_monoid.py.

760c939  Merge branch 'public/monoids/15289indexed' of trac.sagemath.org:sage into public/monoids/15289indexed

03057a4  Merge branch 'develop' into public/monoids/15289indexed

a2996e0  Merge branch 'develop' into public/monoids/15289indexed

c1cc341  Merge branch 'develop' into public/monoids/15289indexed

c7baad9  Merge branch 'public/monoids/15289indexed' into public/algebras/yangians

4fe436f  Merge branch 'public/algebras/yangians' of trac.sagemath.org:sage into public/algebras/yangians

comment:4 Changed 8 years ago by
 Commit changed from 4fe436fc9684176c5eaca8b9063b354b27cc19f8 to c467001c28656ac6ca798c954ea6bc05cf08a959
comment:5 Changed 8 years ago by
 Milestone changed from sage6.2 to sage6.3
comment:6 Changed 8 years ago by
 Commit changed from c467001c28656ac6ca798c954ea6bc05cf08a959 to 0962d33d424449521c7f7c0b00b48b48e8228dce
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

comment:7 Changed 8 years ago by
 Commit changed from 0962d33d424449521c7f7c0b00b48b48e8228dce to d5954ea12138d414b2246cd2ca06017d03bfe492
Branch pushed to git repo; I updated commit sha1. New commits:
d5954ea  Fix from changes in #15289.

comment:8 Changed 8 years ago by
 Commit changed from d5954ea12138d414b2246cd2ca06017d03bfe492 to 629604f104592321a946c3b494b2284e7ff15364
comment:9 Changed 8 years ago by
 Milestone changed from sage6.3 to sage6.4
comment:10 Changed 8 years ago by
 Commit changed from 629604f104592321a946c3b494b2284e7ff15364 to 36d07014aae9c6770b940e27bfdc5ee548f8cdb7
comment:11 Changed 7 years ago by
 Commit changed from 36d07014aae9c6770b940e27bfdc5ee548f8cdb7 to 99a92e3fe4353507bbb650fd1dcf1cf6f82aa3a4
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
25c0fbc  looked through clifford_algebra and filtered_algebras*; many TODOs left

2a62c3b  lift_* methods in algebras/clifford_algebra.py should remember the gradedfiltered choice

15cf0dc  fix and a first doctest for induced_graded_map

5029956  another pitfall documented

292ef5f  another doctest

c2e84e1  remaining doctests for induced_graded_map

03bd4cf  possibly controversial: graded_algebra and the three methods forming its interface are now cached_methods

8a747c0  further edits

237daea  Merge branch 'public/categories/filtered_algebras17096' of trac.sagemath.org:sage into public/algebras/yangians

99a92e3  Added to catalog and refactored over #17096.

comment:12 Changed 7 years ago by
 Dependencies changed from #10963 #15289 to #10963 #15289 #17096
 Description modified (diff)
Refactored over #17096.
comment:13 Changed 7 years ago by
 Commit changed from 99a92e3fe4353507bbb650fd1dcf1cf6f82aa3a4 to 1770d3f50ac68932605fecbd0708d2a413d6f2f3
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)

570bc49  Merge branch 'public/categories/super_categories18044' into 6.9.b1

b91cd82  trac #18044 correct one typo in the doc

7fd1df2  Merge branch 'public/categories/super_categories18044' of trac.sagemath.org:sage into public/categories/super_categories18044

0579337  Some reviewer tweaks and doc additions.

aec22cc  Added one more test.

4b2046f  Merge branch 'public/categories/super_categories18044' into public/categories/filtered_algebras17096

3f67b6b  Fixing trivial doctest due to changes in category heirarchy.

fa476dd  Fixing doublecolon in INPUT block.

1770d3f  Merge branch 'public/algebras/yangians' of trac.sagemath.org:sage into public/algebras/yangians

comment:14 Changed 6 years ago by
 Branch changed from public/algebras/yangians to public/algebras/yangians15484
 Commit changed from 1770d3f50ac68932605fecbd0708d2a413d6f2f3 to ea127f16470d0921d7b11272ad37c7c017e03a21
 Dependencies #10963 #15289 #17096 deleted
 Milestone changed from sage6.4 to sage6.11
New commits:
976c3a5  imported patch yangiansts.patch

446e08b  Fixes for Yangian.

6d21520  Added doctests to full coverage.

b0c1bd1  Fix from changes in #15289.

62acea7  Some output tweaks.

03281d0  Many fixes for Yangians and added to the documentation.

f5e13bc  Added associated graded algebras to the Yangians.

8ce5567  Added to catalog and refactored over #17096.

ea127f1  Fixing the Yangian due to recent changes in Sage.

comment:15 Changed 6 years ago by
 Commit changed from ea127f16470d0921d7b11272ad37c7c017e03a21 to 6b8bcd3f351d9abd7ffd86e7b307c952f356f5ad
Branch pushed to git repo; I updated commit sha1. New commits:
6b8bcd3  Merge branch 'public/algebras/yangians15484' of trac.sagemath.org:sage into public/algebras/yangians15484

comment:16 Changed 6 years ago by
 Milestone changed from sage7.0 to sage7.2
comment:17 Changed 6 years ago by
 Status changed from needs_review to needs_work
See patchbot (note that I don't personally care about this ticket, sorry)
comment:18 Changed 6 years ago by
 Commit changed from 6b8bcd3f351d9abd7ffd86e7b307c952f356f5ad to f297f3342642227be034b564356494a06c2863e0
comment:19 Changed 6 years ago by
 Status changed from needs_work to needs_review
I understand; thanks for the headsup.
comment:20 followup: ↓ 21 Changed 6 years ago by
 Cc andrew.mathas added
 Milestone changed from sage7.2 to sage7.4
Just in case you're interested Andrew.
comment:21 in reply to: ↑ 20 Changed 6 years ago by
 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 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 changed from f297f3342642227be034b564356494a06c2863e0 to ec4e344d7216c91d84aa5aae3c6342098d232d1d
Branch pushed to git repo; I updated commit sha1. New commits:
ec4e344  Added references.

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 5 years ago by
 Commit changed from ec4e344d7216c91d84aa5aae3c6342098d232d1d to 8227771648f9603fb8f1fb66baa42fd74dae1bd7
Branch pushed to git repo; I updated commit sha1. New commits:
8227771  Merge branch 'public/algebras/yangians15484' in 7.5.b6

comment:26 Changed 5 years ago by
 Commit changed from 8227771648f9603fb8f1fb66baa42fd74dae1bd7 to 5336becc00f10520678ef396676b8f50e2f283d3
comment:27 Changed 5 years ago by
 Commit changed from 5336becc00f10520678ef396676b8f50e2f283d3 to 8aa9ef9bde3adb3172b1234e27e384e9f786da09
comment:28 Changed 5 years ago by
 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 5 years ago by
 Milestone changed from sage7.4 to sage8.0
comment:30 Changed 5 years ago by
Looks good. :)
comment:31 Changed 5 years ago by
 Commit changed from 8aa9ef9bde3adb3172b1234e27e384e9f786da09 to 9b977989bc1f2fb15852beb1780bb7d5e0c0da6a
Branch pushed to git repo; I updated commit sha1. New commits:
9b97798  More documentation additions

comment:32 followup: ↓ 33 Changed 5 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 Rmatrix also be added to this module?
comment:33 in reply to: ↑ 32 Changed 5 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 Rmatrix also be added to this module?
It would make for a good followup.
comment:34 Changed 5 years ago by
 Commit changed from 9b977989bc1f2fb15852beb1780bb7d5e0c0da6a to f26834b2c03f0565c0a97145b15002b22ff80ff2
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
e0f9c88  Use monomial_coefficients instead of iteration for consistancy.

f61aae2  Better mutliplication of PBW elements.

9cea97d  Merge branch 'public/lie_algebras/pbw_mult_monomial_coeffs23268' into public/algebras/yangians15484

35aa493  Added monomial_coefficients for gl.

eb19d0e  Merge branch 'public/lie_algebras/monomial_gl23267' into public/algebras/yangians15484

a89bfcc  Adding an additional doctest checking U(gl_n) homomorphism.

5d87394  Trivial doctest fixes.

707c5f1  Merge branch 'public/linear_algebra/matrix_space_with_basis22955' into public/algebras/yangians15484

522d374  Adding Filtered category to PBW basis.

f26834b  Merge branch 'public/lie_algebras/pbw_filtered23270' into public/algebras/yangians15484

comment:35 Changed 5 years ago by
 Dependencies set to #23266, #23267, #23268, #23270
comment:36 Changed 5 years ago by
 Commit changed from f26834b2c03f0565c0a97145b15002b22ff80ff2 to 5967289e2895e9be0b62af1ad5844e2c0d044c12
Branch pushed to git repo; I updated commit sha1. New commits:
5967289  Fixing typo antipode > counit.

comment:37 Changed 5 years ago by
 Commit changed from 5967289e2895e9be0b62af1ad5844e2c0d044c12 to adb8d979e4deadb96749b87861cb3d0fea8370d7
Branch pushed to git repo; I updated commit sha1. New commits:
adb8d97  Fixed documentation errors

comment:38 Changed 5 years ago by
 Commit changed from adb8d979e4deadb96749b87861cb3d0fea8370d7 to 8051da25618f5275384196e7d5236386f7c06584
comment:39 Changed 5 years ago by
 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 5 years ago by
 Branch changed from public/algebras/yangians15484 to 8051da25618f5275384196e7d5236386f7c06584
 Resolution set to fixed
 Status changed from positive_review to closed
Last 10 new commits: