#15806: Integrable representations of (affine) Kac-Moody Lie Algebras
-------------------------------------+-------------------------------------
Reporter: bump | Owner: bump
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: combinatorics | Resolution:
Keywords: Kac-Moody, | Merged in:
Integrable Representation, Affine | Reviewers:
Lie Algebra | Work issues: The dominant_maximal
Authors: bump | method will be reimplemented.
Report Upstream: N/A | Commit:
Branch: | 0aa8bb15e816f904bfff506453b7ef5721806a70
public/combinat/integrable-15806 | Stopgaps:
Dependencies: |
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Comment (by tscrim):
Here's some code which to get all weights in the `lvl`-dilated dominant
chamber:
{{{
sage: P = RootSystem(['A',4,1]).weight_lattice(extended=True)
sage: La = P.fundamental_weights()
sage: lvl = 3
sage: def next_level(wt):
return [wt + la for la in La if (wt+la).level() < lvl]
....:
sage: R = RecursivelyEnumeratedSet([P.zero()], next_level)
sage: list(R)
[0,
Lambda[2],
Lambda[4],
Lambda[1],
Lambda[3],
Lambda[0],
Lambda[3] + Lambda[4],
2*Lambda[0],
Lambda[2] + Lambda[4],
2*Lambda[1],
Lambda[2] + Lambda[3],
Lambda[1] + Lambda[2],
Lambda[1] + Lambda[3],
Lambda[1] + Lambda[4],
2*Lambda[2],
Lambda[0] + Lambda[4],
Lambda[0] + Lambda[1],
Lambda[0] + Lambda[3],
Lambda[0] + Lambda[2],
2*Lambda[4],
2*Lambda[3]]
}}}
if you just want the classical fundamental weights, then do:
{{{
sage: La = [P.fundamental_weight(i) for i in P.index_set() if i != 0]
sage: R = RecursivelyEnumeratedSet([P.zero()], next_level)
sage: list(R)
[0,
Lambda[2],
Lambda[4],
Lambda[1],
Lambda[3],
Lambda[3] + Lambda[4],
Lambda[2] + Lambda[4],
2*Lambda[1],
Lambda[2] + Lambda[3],
Lambda[1] + Lambda[2],
Lambda[1] + Lambda[3],
Lambda[1] + Lambda[4],
2*Lambda[2],
2*Lambda[4],
2*Lambda[3]]
}}}
I'm not sure how to check if it's in the right coset off-hand.
--
Ticket URL: <http://trac.sagemath.org/ticket/15806#comment:33>
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