#14143: alcove model in affine cartan type
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Reporter: alubovsky | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.10
Component: combinatorics | Resolution:
Keywords: alcove model, days45 | Work issues:
Report Upstream: N/A | Reviewers: Anne Schilling,
Authors: Arthur Lubovsky | Merged in:
Dependencies: | Stopgaps:
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Comment (by aschilling):
Hi Arthur, again,
There were some small glitches in the documentation which I fixed in a
review patch on the sage-combinat queue. If you are happy with those,
please fold it into your patch.
Also, you mentioned that CrystalOfAlcovePath now has the same entries as
LittelmannPath. However, you did not change the documentation of the input
to reflect this. Could you please do so? Also, you will need to add some
examples such as
{{{
sage: R = RootSystem(['A',2])
sage: P = R.weight_lattice()
sage: La = P.fundamental_weights()
sage: CrystalOfAlcovePaths(La[1])
Highest weight crystal of alcove paths of type ['A', 2] and weight
Lambda[1]
sage: C = CrystalOfAlcovePaths(La[1])
sage: B = CrystalOfAlcovePaths(['A',2],[1,0])
sage: B==C
True
}}}
Is the following really the correct behavior? Do you want alcove paths
crystal labeled by level zero weights to be highest weight crystals?
{{{
sage: R = RootSystem(['A',2,1])
sage: P = R.weight_lattice()
sage: La = P.fundamental_weights()
sage: C = CrystalOfAlcovePaths(La[1]-La[0])
sage: C
Highest weight crystal of alcove paths of type ['A', 2, 1] and weight
-Lambda[0] + Lambda[1]
}}}
Best,
Anne
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14143#comment:9>
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