#9123: implement Schur algebras and use them to determine irreducible characters
for GL_n
-------------------------------------+-------------------------------------
Reporter: hthomas | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.7
Component: algebra | Resolution:
Keywords: days30, schur | Merged in:
Authors: Hugh Thomas | Reviewers: Travis Scrimshaw
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/combinat/schur_algebras-9123| 08861457389919f62fae8a1f2eaf0679e939e8f5
Dependencies: | Stopgaps:
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Changes (by tscrim):
* commit: ccc6e3dc31ca4299a679efe4881988afb1f4961d =>
08861457389919f62fae8a1f2eaf0679e939e8f5
* branch: u/chapoton/9123 => public/combinat/schur_algebras-9123
* reviewer: => Travis Scrimshaw
Comment:
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:
||[http://git.sagemath.org/sage.git/commit/?id=cd6a977f9ddbf1ac7b0c3424cd280b683aca802b
cd6a977]||{{{Merge branch 'u/chapoton/9123' of trac.sagemath.org:sage into
public/combinat/schur_algebras-9123}}}||
||[http://git.sagemath.org/sage.git/commit/?id=66b28b1f0fe3bcbd743aecd4dc7f6c0bdf069b48
66b28b1]||{{{Changing indexing set of SchurAlgebra and implementation of
TensorSpace.}}}||
||[http://git.sagemath.org/sage.git/commit/?id=08861457389919f62fae8a1f2eaf0679e939e8f5
0886145]||{{{Some futher cleanup and speedups.}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/9123#comment:12>
Sage <http://www.sagemath.org>
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