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Implement Yangian for gl(n) #15484

Closed tscrim closed 7 years ago

tscrim commented 10 years ago

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.

Depends on #23266 Depends on #23267 Depends on #23268 Depends on #23270

CC: @sagetrac-sage-combinat @anneschilling @darijgr @bsalisbury1

Component: algebra

Keywords: yangian, quantum groups

Author: Travis Scrimshaw

Branch/Commit: 8051da2

Reviewer: Ben Salisbury

Issue created by migration from https://trac.sagemath.org/ticket/15484

tscrim commented 10 years ago

Changed branch from public/algebras/yangian to public/algebras/yangians

tscrim commented 10 years ago

Last 10 new commits:

[63f89cb](https://github.com/sagemath/sagetrac-mirror/commit/63f89cb)Added doctests to full coverage.
[cd3e53e](https://github.com/sagemath/sagetrac-mirror/commit/cd3e53e)Merge branch 'public/monoids/15289-indexed' into u/tscrim/yangians
[9dca526](https://github.com/sagemath/sagetrac-mirror/commit/9dca526)Added comparison operations.
[a493bee](https://github.com/sagemath/sagetrac-mirror/commit/a493bee)Merge branch 'master' into public/monoids/15289-indexed
[7e39c1f](https://github.com/sagemath/sagetrac-mirror/commit/7e39c1f)Fixes for Yangian.
[bc1b55c](https://github.com/sagemath/sagetrac-mirror/commit/bc1b55c)Merge branch 'public/monoids/15289-indexed' into u/tscrim/yangians
[435a303](https://github.com/sagemath/sagetrac-mirror/commit/435a303)Merge branch 'public/ticket/10963' of ssh://trac.sagemath.org:2222/sage into u/tscrim/yangians
[80d55fe](https://github.com/sagemath/sagetrac-mirror/commit/80d55fe)merging sage/categories/category.py
[b2064e6](https://github.com/sagemath/sagetrac-mirror/commit/b2064e6)Merge branch 'u/tscrim/yangians' of ssh://trac.sagemath.org:2222/sage into u/tscrim/yangians
[b113acc](https://github.com/sagemath/sagetrac-mirror/commit/b113acc)Merge branch 'master' into u/tscrim/yangians
tscrim commented 10 years ago

Commit: 63f89cb

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Changed commit from 63f89cb to 4fe436f

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

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
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Changed commit from 4fe436f to c467001

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

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
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Changed commit from c467001 to 0962d33

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

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
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

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

d5954eaFix from changes in #15289.
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Changed commit from 0962d33 to d5954ea

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

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.
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from d5954ea to 629604f

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

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.
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 629604f to 36d0701

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

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.
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 36d0701 to 99a92e3

tscrim commented 9 years ago
comment:12

Refactored over #17096.

tscrim commented 9 years ago

Description changed:

--- 
+++ 
@@ -1 +1 @@
-
+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.
tscrim commented 9 years ago

Changed dependencies from #10963 #15289 to #10963 #15289 #17096

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 99a92e3 to 1770d3f

tscrim commented 8 years ago

Changed commit from 1770d3f to ea127f1

tscrim commented 8 years ago

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.
tscrim commented 8 years ago

Changed branch from public/algebras/yangians to public/algebras/yangians-15484

tscrim commented 8 years ago

Changed dependencies from #10963 #15289 #17096 to none

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from ea127f1 to 6b8bcd3

jdemeyer commented 7 years ago
comment:17

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

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

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.
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from 6b8bcd3 to f297f33

tscrim commented 7 years ago
comment:19

I understand; thanks for the heads-up.

tscrim commented 7 years ago
comment:20

Just in case you're interested Andrew.

AndrewMathas commented 7 years ago
comment:21

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...

darijgr commented 7 years ago
comment:22

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 :)

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

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

ec4e344Added references.
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from f297f33 to ec4e344

tscrim commented 7 years ago
comment:24

Andrew, no problem.

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

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

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

8227771Merge branch 'public/algebras/yangians-15484' in 7.5.b6
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from ec4e344 to 8227771

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

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.
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from 8227771 to 5336bec

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

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
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from 5336bec to 8aa9ef9

bsalisbury1 commented 7 years ago

Reviewer: Ben Salisbury

bsalisbury1 commented 7 years ago
comment:28

Hi Travis,

I added some more to the documentation. Please make sure you are okay with it. I will continue the review soon.

Ben

tscrim commented 7 years ago
comment:30

Looks good. :)

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from 8aa9ef9 to 9b97798

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

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

9b97798More documentation additions
bsalisbury1 commented 7 years ago
comment:32

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: