Opened 11 years ago

Closed 6 years ago

#9123 closed enhancement (fixed)

implement Schur algebras and use them to determine irreducible characters for GL_n

Reported by: hthomas Owned by: AlexGhitza
Priority: major Milestone: sage-6.7
Component: algebra Keywords: days30, schur
Cc: QuantumKing Merged in:
Authors: Hugh Thomas Reviewers: Travis Scrimshaw, Frédéric Chapoton
Report Upstream: N/A Work issues:
Branch: af7795e (Commits, GitHub, GitLab) Commit: af7795e4ceba74f0ede849ab4f73e64c789f6ad8
Dependencies: Stopgaps:

Status badges

Description (last modified by hthomas)

Schur algebras are used in the description of the representation theory of GL_n. I plan to implement them, and use them to calculate the characters of the irreducible modules of GL_n (in characteristic p).

A nice reference is Green's book "Polynomial representations of GL_n".

Attachments (1)

trac_9123-schur-algebra-and-gln-characters-ht.patch (18.7 KB) - added by hthomas 8 years ago.

Download all attachments as: .zip

Change History (22)

comment:1 Changed 11 years ago by hthomas

  • Owner changed from AlexGhitza to hthomas

comment:2 Changed 10 years ago by hthomas

  • Cc sage-combinat removed
  • Description modified (diff)
  • Keywords days30 added
  • Owner changed from hthomas to AlexGhitza
  • Summary changed from implement Schur algebras using AlgebrasWithBasis to implement Schur algebras and use them to determine irreducible characters for GL_n

comment:3 Changed 10 years ago by hthomas

A patch which does more or less what I want is on the sage-combinat queue, but it needs more work on the documentation. I was told I shouldn't post it here until I had that done, but if anyone wants to look at it other than by installing the combinat queue, I would be happy to post it.

comment:4 Changed 8 years ago by hthomas

Someone expressed interest in seeing the current state of the code, so I have attached it.

comment:5 Changed 8 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:6 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:7 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:8 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:9 Changed 6 years ago by chapoton

  • Branch set to u/chapoton/9123
  • Commit set to a051cedd863487bb61b317b4b1a537607ff481e7
  • Keywords schur added
  • Milestone changed from sage-6.4 to sage-6.7
  • Status changed from new to needs_review

Here is a git branch. Tests do pass, but the doc may not build.


New commits:

fcb7e48No Subject. Modified: algebra.rst, all.py, general_linear.py, schur_algebra.py
a051cedtrac #9123 cleaning the file

comment:10 Changed 6 years ago by git

  • Commit changed from a051cedd863487bb61b317b4b1a537607ff481e7 to ce20f4a20cddde7f2287fd6c9b5c692ab0fa15ce

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

ce20f4atrac #9123 simplify the logic a bit

comment:11 Changed 6 years ago by git

  • Commit changed from ce20f4a20cddde7f2287fd6c9b5c692ab0fa15ce to ccc6e3dc31ca4299a679efe4881988afb1f4961d

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

ccc6e3dtrac #9123 correct one

comment:12 Changed 6 years ago by tscrim

  • Branch changed from u/chapoton/9123 to public/combinat/schur_algebras-9123
  • Commit changed from ccc6e3dc31ca4299a679efe4881988afb1f4961d to 08861457389919f62fae8a1f2eaf0679e939e8f5
  • Reviewers set to Travis Scrimshaw

I made a bunch of major revisions:

  • I changed the indexing set for SchurAlgebra be tuples rather than words since it was not using any properties of words and was incurring for it.
  • I changed TensorSpace to SchurTensorModule (although I'm quite open to better names).
  • SchurTensorModule inherits from CombinatorialFreeModule_Tensor. This makes it behave like a tensor product with respect to things like tensor().
  • I implemented the actions of the symmetric group (well...permutations), the symmetric group algebra, and the Schur algebra as actual actions using _acted_upon_. I also cached the Schur action morphism and implemented the permutation actions directly.
  • Renamed GL_n_irred_character to GL_irreducible_character.
  • Added documentation and doctests for full coverage.

The net result of my changes is over a 30x speedup to GL_irreducible_character, which allowed me to remove the # long time from those tests. If someone (Hugh, Frederic, ?) could review my changes, then I think we can set a positive review.


New commits:

cd6a977Merge branch 'u/chapoton/9123' of trac.sagemath.org:sage into public/combinat/schur_algebras-9123
66b28b1Changing indexing set of SchurAlgebra and implementation of TensorSpace.
0886145Some futher cleanup and speedups.

comment:13 Changed 6 years ago by git

  • Commit changed from 08861457389919f62fae8a1f2eaf0679e939e8f5 to d0b30ccc97b1d3b8bca056d17b9f3730f4f0011e

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

d0b30cctrac #9123 review commit (pep8 and doc corrections)

comment:14 Changed 6 years ago by chapoton

Thanks a lot Travis.

I have made a review patch.

There is still something missing : the doc for SchurTensorModule? is almost void. Nowhere one can see anything about the commuting actions. I think one should at least illustrate both actions.

comment:15 Changed 6 years ago by tscrim

Thanks for those changes. I will add the examples later today.

comment:16 Changed 6 years ago by git

  • Commit changed from d0b30ccc97b1d3b8bca056d17b9f3730f4f0011e to af7795e4ceba74f0ede849ab4f73e64c789f6ad8

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

60f544fAdding some examples and changing the repr of SchurAlgebra elements.
af7795eMerge branch 'public/combinat/schur_algebras-9123' of trac.sagemath.org:sage into public/combinat/schur_algebras-9123

comment:17 Changed 6 years ago by tscrim

Done. I also tweaked the output of the elements of the Schur algebra.

comment:18 Changed 6 years ago by chapoton

Ok, looks good to me. If you see nothing else to do, set to positive review.

comment:19 Changed 6 years ago by tscrim

  • Reviewers changed from Travis Scrimshaw to Travis Scrimshaw, Frédéric Chapoton
  • Status changed from needs_review to needs_work

Thanks Frédéric.

comment:20 Changed 6 years ago by tscrim

  • Status changed from needs_work to positive_review

Helps if I select the right thing...

comment:21 Changed 6 years ago by vbraun

  • Branch changed from public/combinat/schur_algebras-9123 to af7795e4ceba74f0ede849ab4f73e64c789f6ad8
  • Resolution set to fixed
  • Status changed from positive_review to closed
Note: See TracTickets for help on using tickets.