#18398: Automate Branching Rules for IntegrableRepresentations
-------------------------------------+-------------------------------------
Reporter: bump | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.7
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Daniel Bump | Reviewers:
Report Upstream: N/A | Work issues: #18767 should be
Branch: | merged first since it is more
public/combinat/branching-15398 | important
Dependencies: | Commit:
| 1ee0267f7bf4a926a3f6e0295a08be464e2e529f
| Stopgaps:
-------------------------------------+-------------------------------------
Changes (by bump):
* work_issues: => #18767 should be merged first since it is more
important
Comment:
This patch contains a lot of case-by-case encoding of work that can also
be done by hand by the user when the user needs the branching rules
(explained in the reference manual). It saves the reader having to line up
the Dynkin diagrams.
So although it is convenient not to have to do this, the reader who needs
a branching rule can do so without this patch. This patch is therefore
less important than #18767 which adds real new functionality. it should be
extended to the twisted types. Presumably it clashes with #18767 and I
think it is better if #18767 (which adds real new functionality) is merged
first. After that, this patch should be extended to include the twisted
cases.
> In #15463, I go part of the way there by implementing a subtype method,
but I think we should take that idea and expand on it here, and then use
subtype to do the branching rule here.
Following a suggestion of Volker Braun, branching rules for finite
dimensional Lie algebras were implemented in the categorical framework in
the Weyl character ring.
{{{
sage: R1=branching_rule("E7","A7","extended")
sage: type(R1)
<class 'sage.combinat.root_system.branching_rules.BranchingRule'>
sage: R2=branching_rule("A7","A3xA3","levi")
sage: R1*R2
composite branching rule E7 => (extended) A7 => (levi) A3xA3
}}}
One could try to extend this to the affine case but here we are only
dealing with Levi branching rules. (The Levi subalgebras are finite-
dimensional.) This is less ambitious but still useful.
--
Ticket URL: <http://trac.sagemath.org/ticket/18398#comment:6>
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