#18453: Infinite affine crystals should use extended weight lattice
-------------------------------------+-------------------------------------
Reporter: bump | Owner:
Type: defect | Status: needs_work
Priority: major | Milestone: sage-6.8
Component: combinatorics | Resolution:
Keywords: crystals, days65 | Merged in:
Authors: Ben Salisbury, | Reviewers: Dan Bump
Anne Schilling, Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 8e5c4cd07daadb6479b3a6bc18b12d42254a3d74
public/crystal/18453 | Stopgaps:
Dependencies: #18700 |
-------------------------------------+-------------------------------------
Changes (by tscrim):
* dependencies: => #18700
Comment:
Here's the problem:
{{{
sage: La = RootSystem(['A',2,1]).weight_space().basis()
sage: LS = crystals.ProjectedLevelZeroLSPaths(2*La[1])
sage: LS.weight_lattice_realization()
Weight space over the Rational Field of the Root system of type ['A', 2,
1]
sage: CS = LS.one_dimensional_configuration_sum()
sage: CS
B[-2*Lambda[1] + 2*Lambda[2]] + (q+1)*B[-Lambda[1]] + (q+1)*B[Lambda[1] -
Lambda[2]] + B[2*Lambda[1]] + B[-2*Lambda[2]] + (q+1)*B[Lambda[2]]
sage: K = crystals.KirillovReshetikhin(['A',2,1], 1,1)
sage: T = K.tensor(K)
sage: CSK = T.one_dimensional_configuration_sum()
sage: CSK
B[-2*Lambda[1] + 2*Lambda[2]] + (q+1)*B[-Lambda[1]] + (q+1)*B[Lambda[1] -
Lambda[2]] + B[2*Lambda[1]] + B[-2*Lambda[2]] + (q+1)*B[Lambda[2]]
sage: CS == CSK
False
sage: CS.parent()
Group algebra of the Weight space over the Rational Field of the Root
system of type ['A', 2] over Univariate Polynomial Ring in q over Rational
Field
sage: CSK.parent()
Group algebra of the Weight lattice of the Root system of type ['A', 2]
over Univariate Polynomial Ring in q over Rational Field
sage: CS.parent().has_coerce_map_from(CSK.parent())
False
}}}
The group algebra, by its functoriality, should have a coercion when the
underlying groups have a coercion:
{{{
sage: CS.parent()._indices.has_coerce_map_from(CSK.parent()._indices)
True
}}}
This is now #18700.
--
Ticket URL: <http://trac.sagemath.org/ticket/18453#comment:52>
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