Opened 4 years ago

Closed 4 years ago

#25937 closed enhancement (fixed)

Add documentation for integrable representation (#15806) to Lie methods thematic tutorial

Reported by: bump Owned by: bump
Priority: major Milestone: sage-8.4
Component: documentation Keywords: sagedays@icerm
Cc: khlee, aschilling, nthiery, tscrim, bsalisbury1, kdilks Merged in:
Authors: Daniel Bump Reviewers: Anne Schilling, Kyu-Hwan Lee, Travis Scrimshaw
Report Upstream: N/A Work issues:
Branch: a9119bb (Commits, GitHub, GitLab) Commit: a9119bb991c00e817dc01a5c69932f233d2f0feb
Dependencies: Stopgaps:

Status badges

Description

The IntegrableRepresentation? code for working with integrable representations of affine Lie algebras is documented in the reference manual but not in the Lie Methods and Related Combinatorics thematic tutorial. This ticket is to add documentation to the thematic tutorial.

Change History (64)

comment:1 Changed 4 years ago by bump

  • Cc khlee aschilling nthiery tscrim added
  • Owner changed from (none) to bump
  • Type changed from PLEASE CHANGE to enhancement

comment:2 Changed 4 years ago by bump

  • Authors changed from bump to Daniel Bump
  • Branch set to public/tutorial-25937
  • Commit set to 506f2ece770cdd084c18f9feb32465b36b4df1f3

New commits:

506f2ecLie thematic tutorial revisions

comment:3 Changed 4 years ago by bsalisbury1

  • Cc bsalisbury1 added

comment:4 Changed 4 years ago by git

  • Commit changed from 506f2ece770cdd084c18f9feb32465b36b4df1f3 to 1e8dadf561dba8f21d0e1428d5aa874121510452

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

874e575writing about weight lattice, integrable representations, etc.
1e8dadfminor edits

comment:5 Changed 4 years ago by git

  • Commit changed from 1e8dadf561dba8f21d0e1428d5aa874121510452 to 73afeaf3adbc772078c9923897f995106ffff0e5

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

73afeafminor fix

comment:6 Changed 4 years ago by git

  • Commit changed from 73afeaf3adbc772078c9923897f995106ffff0e5 to 19031754641eba0ae8437444114d4d9f0d507fc4

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

1903175mention methods of weight lattice

comment:7 Changed 4 years ago by git

  • Commit changed from 19031754641eba0ae8437444114d4d9f0d507fc4 to 6b85a922f330809bf8b1752d13c2ae19069c5b0e

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

6b85a92some writing

comment:8 Changed 4 years ago by git

  • Commit changed from 6b85a922f330809bf8b1752d13c2ae19069c5b0e to d54d0f87742ab792e8522190d0ed974d1f27869a

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

d54d0f8some edits

comment:9 Changed 4 years ago by git

  • Commit changed from d54d0f87742ab792e8522190d0ed974d1f27869a to 440d8e20505b6b420c7162585658519ed1f500d6

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

440d8e2Coxeter number

comment:10 Changed 4 years ago by kdilks

  • Cc kdilks added

Once this is done, I can look at it for typos, and see how it looks from the perspective of somebody that's not an expert on this stuff. Would probably still need an expert to at least glance over it to make sure nothing is majorly wrong.

comment:11 Changed 4 years ago by aschilling

I would be glad to help review this ticket. Dan, were there sections you wanted me to write? Why have some titles changed from capitals to lower case letters?

comment:12 Changed 4 years ago by tscrim

I am also willing to help with either writing or reviewing too.

comment:13 Changed 4 years ago by git

  • Commit changed from 440d8e20505b6b420c7162585658519ed1f500d6 to d9066be5fb94bf174daa398947acdf5eee667525

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

d9066bereorganization: moved weight rings section and created a new section for integrable representations

comment:14 Changed 4 years ago by git

  • Commit changed from d9066be5fb94bf174daa398947acdf5eee667525 to 83a5de7bb28ae746bb5d2338af4743f51cafc246

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

83a5de7integrable.rst

comment:15 Changed 4 years ago by git

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

06d9be6doc edits and a new method in integrable_representations.py

comment:16 Changed 4 years ago by git

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

cbebbd1minor fixes

comment:17 Changed 4 years ago by git

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9ed2004mult in Integrable example

comment:18 Changed 4 years ago by git

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

943d20eadded mu option to level method in IntegrableRepresentation

comment:19 Changed 4 years ago by git

  • Commit changed from 943d20e44f9b72abc02a5091d17a29f22c050ed1 to 04e3f60f2531588bf3a56757dd66683e01eb3e41

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

04e3f60string functions

comment:20 Changed 4 years ago by tscrim

I would not have level take an optional weight in the IntegrableRepresentation. Weights already know about their level:

sage: La = RootSystem(['A',3,1]).weight_lattice().fundamental_weights()
sage: (La[2]+La[0]).level()
2
sage: al = RootSystem(['A',3,1]).root_lattice().simple_roots()
sage: al[1].level()
0
sage: La = RootSystem(['A',3,1]).ambient_space().fundamental_weights()
sage: La[1].level()
1

comment:21 Changed 4 years ago by git

  • Commit changed from 04e3f60f2531588bf3a56757dd66683e01eb3e41 to cef780ab800ef422f323a877aa8b1d864495c9f0

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

cef780aintegrable.rst

comment:22 Changed 4 years ago by git

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

d595425changes found by khlee

comment:23 Changed 4 years ago by git

  • Commit changed from d59542577f1b93cb4c13a9fb6b10144b3e2f8041 to f40bb29a9a5dd8124b863f5bfd99006355df8a3a

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f40bb29more about modular characteristics

comment:24 Changed 4 years ago by git

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240c8a8correction

comment:25 Changed 4 years ago by git

  • Commit changed from 240c8a82b1220d329b4ccc6ab6eb830ef5dff710 to 0261f9921cc6159c4ec664c9e4d939d94d83286a

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

0261f99finished 2Lambda[0] example

comment:26 Changed 4 years ago by git

  • Commit changed from 0261f9921cc6159c4ec664c9e4d939d94d83286a to 07c97545a75ca394cba85d6782f6235e265d4ffc

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

07c9754added some examples from khlee

comment:27 Changed 4 years ago by bump

  • Status changed from new to needs_review

comment:28 Changed 4 years ago by bump

A link to the built documentation may be found at:

http://sporadic.stanford.edu/thematic_tutorials/lie.html

The new sections are called "Affine Root System Basics" and "Integrable Highest Weight Representations of Affine Lie algebras".

comment:29 Changed 4 years ago by aschilling

I have trouble checking out the branch. It says that the apply fails. Also the branch is currently red.

Some minor comments in the meantime:

  • 'lie Group Basics' should be 'Lie Group Basics' in the index
  • 'infinity crystals' should be 'Infinity crystals' in the index

comment:30 follow-up: Changed 4 years ago by aschilling

Since I cannot check out the branch, I cannot make these trivial changes. But here are some more typos:

  • othrwise -> otherwise in the section "Untwisted Affine Kac-Moody Lie Algebras"
  • I would use \ldots rather than \cdots in lists
  • alpha_1 should be \alpha_1 in the section "Twisted Types"
  • spce -> space in the section "Roots and Weights"
  • The following sentence "(For the twisted cases, see [Kac]" seems unfinished or a bracket is missing.
  • The link ~sage.combinat.root_system.extended_affine_weyl_group seems broken.

comment:31 Changed 4 years ago by git

  • Commit changed from 07c97545a75ca394cba85d6782f6235e265d4ffc to 55577f7cc791bf62bc35be9fbd120993d2b13b72

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

55577f7Merge branch 'public/tutorial-25937' of git://trac.sagemath.org/sage into public/tutorial-25937

comment:32 Changed 4 years ago by tscrim

I've merged in 8.4.beta0 (which just had a trivial conflict).

comment:33 in reply to: ↑ 30 ; follow-up: Changed 4 years ago by bump

Replying to aschilling:

What happens when you try to check out the branch? I can check it out after first pulling from the develop branch, then:

git checkout origin/public/tutorial-25937 -b tutorial-25937

comment:34 follow-up: Changed 4 years ago by bump

Work issues:

Anne and Travis have some comments that need to be addressed. I'll try to do those now.

Should the section on affine crystals have any references back to this section? Specifically I discuss the question of extended versus not extended root lattice.

We had discussed adding material about Kac and BKK crystals in a new section. That could be another ticket or it could be part of this one.

I have trouble making the backward link to the reference manual on extended affine Weyl groups work at the very end of affine.rst. S similar link to the reference manual for IntegrableRepresentation? class works fine.

comment:35 Changed 4 years ago by git

  • Commit changed from 55577f7cc791bf62bc35be9fbd120993d2b13b72 to 73986ab8b7659898f13acdd3f03b8cb522314f45

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

73986abrevert level method of IntegrableRepresentations

comment:36 in reply to: ↑ 33 Changed 4 years ago by aschilling

Replying to bump:

Replying to aschilling:

What happens when you try to check out the branch? I can check it out after first pulling from the develop branch, then:

git checkout origin/public/tutorial-25937 -b tutorial-25937

Travis rebased the branch. Now I can check it out. Before that did not work for me.

comment:37 Changed 4 years ago by khlee

Here are some corrections of typos and comments on "Integrable Highest..."


second paragraph: weight decomposition --> weight space decomposition

--The support of an integrable highest weight representation

first and second paragraphs: Both \Lambda and \lambda are used. We need to choose one. For consistency, \Lambda is better.

third paragraph: a increasing sequence --> an increasing sequence

---Modular Forms

first paragraph: weakly modular form --> weakly holomorphic modular form

I think that "weakly holomorphic" is more commonly used.

first paragraph: weakly modular means --> weakly holomorphic means

third paragraph: weakly modular form --> weakly holomorphic modular form

third paragraph: the number of positive roots of $\mathfrak g\circ$ --> the number of positive roots plus half the rank of $\mathfrak g\circ$

---Sage methods for integrable representations

first paragraph: highest weight Lie algebras --> highest weight representations

second paragraph: two dominant multiple weights --> two dominant maximal weights

second paragraph: Since $s_0$ fixes $2 \Lambda_1 -\delta$, it is not a good example. The following Sage code does not show the action of the Weyl group element. It may be a good idea to remove the part "We apply...the corresponding dominant maximal weight" as this point will be illustrated in the next paragraph.

fourth paragraph: Again, the choice of $s_0$ is not good. Any other choice will work.

sixth paragraph: the parentheses in the denominator of the first product is broken.

sixth paragraph: the factor $q{-1/8}$ --> the factor $q{1/8}$

seventh(?) paragraph: The infinite sums in the parentheses for the string functions need to begin $1$ instead of $q$.

seventh(?) paragraph: both weakly modular forms --> both weakly holomorphic modular forms

seventh(?) paragraph: two is als a weakly modular form--> two is also a weakly holomorphic modular form

A period is missing after [KimLeeOh2017].

comment:38 in reply to: ↑ 34 ; follow-up: Changed 4 years ago by aschilling

Replying to bump:

Work issues:

Anne and Travis have some comments that need to be addressed. I'll try to do those now.

Should the section on affine crystals have any references back to this section?

Yes, that would be good!

We had discussed adding material about Kac and BKK crystals in a new section. That could be another ticket or it could be part of this one.

Let us make that another ticket unless you want to write these sections now.

comment:39 Changed 4 years ago by git

  • Commit changed from 73986ab8b7659898f13acdd3f03b8cb522314f45 to 1e1802b34248091a8c49d3633b1770b1f4d3e92d

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

1e1802baddressed comments by Travis, Anne and Kyu-Hwan

comment:40 in reply to: ↑ 38 Changed 4 years ago by tscrim

Replying to aschilling:

Replying to bump:

We had discussed adding material about Kac and BKK crystals in a new section. That could be another ticket or it could be part of this one.

Let us make that another ticket unless you want to write these sections now.

I think it would be better to have that as a second ticket anyways (better granularity of purpose on each ticket).

comment:41 Changed 4 years ago by git

  • Commit changed from 1e1802b34248091a8c49d3633b1770b1f4d3e92d to 9099c2e4c6d67db8fd1ef0fec6d7f30ce8198830

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

9282d8eFixes to mult and added a few more doctests.
9099c2eFixes for formatting, typos, and conventions.

comment:42 Changed 4 years ago by tscrim

  • Reviewers set to Anne Schilling, Kyu-Hwan Lee, Travis Scrimshaw

Thank you again Dan for your work on this and improving Sage's documentation/tutorials as a learning resource.

I have made a bunch of small changes in the tutorials. Most of them are small formatting changes and typo fixes, but for a few of my changes, I added a little more detail or did some rewording.

I am happy with the current state.

comment:43 Changed 4 years ago by bump

Can anyone figure out how to make the link at the end of the section on Extended Affine Weyl Groups work?

There is a similar link to the reference manual for the IntegrableRepresentation? class and that works.

The broken link is the very last thing here: http://sporadic.stanford.edu/thematic_tutorials/lie/affine.html

Last edited 4 years ago by bump (previous) (diff)

comment:44 Changed 4 years ago by tscrim

Did you try :mod:`~sage.combinat....`?

I can build the docs, but I can't look at the compiled version until I get to my desktop on Monday.

comment:45 Changed 4 years ago by tscrim

I just realized that I missed something with formatting in integrable.rst (line 269):

 .. MATH::
 
     \begin{aligned}
-    c^{2\Lambda_0}_{2\Lambda_0} & = q^{-1/16}(1+q+3q^2+5q^3+10q^4+16q^5+\cdots),
+    c^{2\Lambda_0}_{2\Lambda_0} & = q^{-1/16}(1+q+3q^2+5q^3+10q^4+16q^5+\cdots), \\
     c^{2\Lambda_0}_{2\Lambda_1-\delta} & = q^{7/16}(1+2q+4q^2+7q^3+13q^4+21q^5+\cdots).
     \end{aligned}

I can push this change if you want.

comment:46 Changed 4 years ago by tscrim

In addition to A001700, it may also be worthwhile mentioning the doubled version: A128015. Thoughts?

comment:47 Changed 4 years ago by git

  • Commit changed from 9099c2e4c6d67db8fd1ef0fec6d7f30ce8198830 to 61c899260dd18ac3b819dc3626ef61a2a756457b

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

61c89923 comments by Travis

comment:48 Changed 4 years ago by bump

Did you try :mod:~sage.combinat....?

That works. Thanks!

I implemented the last 3 comments from Travis and pushed.


New commits:

61c89923 comments by Travis

comment:49 Changed 4 years ago by tscrim

No problem.

Anyone else have any comments? (Kevin?) I am ready to set this to a positive review.

comment:50 Changed 4 years ago by khlee

I have read the document one more time and found a few typos. After correcting them, I would agree to set this to a positive review. Thanks!!


--The support of an integrable highest weight representation

first paragraph: $L(\lambda)$ --> $L(\Lambda)$ (There are two occurrences of this.)

---Sage methods for integrable representations

first paragraph: A period is missing at the end of the last sentence.

second paragraph: The sentence "Then we compute the string function at this weight, which we see agrees with the string function for the corresponding dominant maximal weight:" seems out of place. Could we delete it?

A period is missing at the end of the displayed math in the sentence begin with "Reading what the OEIS..."

The formulas of two string functions are not adequately aligned.


comment:51 Changed 4 years ago by git

  • Commit changed from 61c899260dd18ac3b819dc3626ef61a2a756457b to b0479960caba0f8c0fd92f64180e8be6d1310aa7

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

b047996comments by khlee

comment:52 Changed 4 years ago by bump

I made Kyu-Hwan's corrections except this one:

The formulas of two string functions are not adequately aligned.

I don't see the alignment problem.


New commits:

b047996comments by khlee

comment:53 Changed 4 years ago by aschilling

In the introduction to "Integrable Highest Weight Representations of Affine Lie algebras", there is still a missing link:

weyl_character_ring

comment:54 Changed 4 years ago by aschilling

The link to the last OESIS 'OEIS sequence 128015' seems broken. Other than these last two link problems, I am also happy to set a positive review.

comment:55 Changed 4 years ago by kdilks

@Travis it seems like enough other people have already gotten a chance to read through it.

comment:56 Changed 4 years ago by git

  • Commit changed from b0479960caba0f8c0fd92f64180e8be6d1310aa7 to cb48b6c187680ef762fcaebf9362610891432e5e

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

cb48b6ctwo broken links found by Anne

comment:57 Changed 4 years ago by khlee

I am not sure what happened to the alignment problem. In any case, it disappeared, and I am happy with the current version.

comment:58 Changed 4 years ago by git

  • Commit changed from cb48b6c187680ef762fcaebf9362610891432e5e to adbc210150915d9c238fc8f6da3c68163fc227ed

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

adbc210two more typos

comment:59 Changed 4 years ago by aschilling

  • Status changed from needs_review to positive_review

comment:60 Changed 4 years ago by vbraun

  • Status changed from positive_review to needs_work

Should be marked as optional internet:

File "src/doc/en/thematic_tutorials/lie/integrable.rst", line 224, in doc.en.thematic_tutorials.lie.integrable
Failed example:
    [oeis(x) for x in V.strings().values()]
Exception raised:
    Traceback (most recent call last):
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 614, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 1025, in compile_and_execute
        exec(compiled, globs)
      File "<doctest doc.en.thematic_tutorials.lie.integrable[12]>", line 1, in <module>
        [oeis(x) for x in V.strings().values()]
      File "sage/misc/lazy_import.pyx", line 354, in sage.misc.lazy_import.LazyImport.__call__ (build/cythonized/sage/misc/lazy_import.c:3759)
        return self.get_object()(*args, **kwds)
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/databases/oeis.py", line 382, in __call__
        return self.find_by_subsequence(query, max_results, first_result)
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/databases/oeis.py", line 510, in find_by_subsequence
        return self.find_by_description(subsequence, max_results, first_result)
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/databases/oeis.py", line 475, in find_by_description
        sequence_list = _fetch(url).split('\n\n')[2:-1]
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/databases/oeis.py", line 195, in _fetch
        raise IOError("%s\nError fetching %s." % (msg, url))
    IOError: <urlopen error [Errno 60] Operation timed out>
    Error fetching http://oeis.org/search?q=1%2C+1%2C+3%2C+5%2C+10%2C+16%2C+28%2C+43%2C+70%2C+105%2C+161%2C+236&start=0&fmt=text&n=3.
**********************************************************************
1 item had failures:
   1 of  32 in doc.en.thematic_tutorials.lie.integrable
    [31 tests, 1 failure, 131.65 s]
----------------------------------------------------------------------
sage -t --long src/doc/en/thematic_tutorials/lie/integrable.rst  # 1 doctest failed
---------------------------------------------------------------------

comment:61 Changed 4 years ago by git

  • Commit changed from adbc210150915d9c238fc8f6da3c68163fc227ed to a9119bb991c00e817dc01a5c69932f233d2f0feb

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

a9119bboeis test is optional internet

comment:62 Changed 4 years ago by bump

  • Status changed from needs_work to needs_review

This had a positive review. Per comment:60 I changed the oeis test to optional -- internet. I was unsure whether it is appropriate for me to put the positive review back so I changed it to needs review.

comment:63 Changed 4 years ago by aschilling

  • Status changed from needs_review to positive_review

comment:64 Changed 4 years ago by vbraun

  • Branch changed from public/tutorial-25937 to a9119bb991c00e817dc01a5c69932f233d2f0feb
  • Resolution set to fixed
  • Status changed from positive_review to closed
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