#18453: Infinite affine crystals should use extended weight lattice
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Reporter: bump | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: combinatorics | Resolution:
Keywords: crystals | Merged in:
Authors: Ben Salisbury, | Reviewers:
Anne Schilling, Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 7963ea6a64dc4bd1d623288fbb6702e11beae0dc
public/crystal/18453 | Stopgaps:
Dependencies: |
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Comment (by aschilling):
Replying to [comment:17 nthiery]:
> Replying to [comment:8 aschilling]:
> > I had to fix the Weyl dimension formula (which I guess was written by
Nicolas and only worked in the ambient space).
>
> By Dan, if I recall correctly.
{{{
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 859) def
weyl_dimension(self, highest_weight):
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 860)
"""
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 861)
EXAMPLES::
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 862)
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 863)
sage: RootSystem(['A',3]).ambient_lattice().weyl_dimension([2,1,0,0])
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 864)
20
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 865)
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 866)
sage:
type(RootSystem(['A',3]).ambient_lattice().weyl_dimension([2,1,0,0]))
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 867)
<type 'sage.rings.integer.Integer'>
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 868)
"""
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 869)
highest_weight = self(highest_weight)
f562ca2b (Travis Scrimshaw 2014-10-01 17:16:31 -0700 870) if
not highest_weight.is_dominant():
f562ca2b (Travis Scrimshaw 2014-10-01 17:16:31 -0700 871)
raise ValueError("the highest weight must be dominant")
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 872)
rho = self.rho()
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 873) n
= prod([(rho+highest_weight).dot_product(x) for x in
self.positive_roots()])
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 874) d
= prod([ rho.dot_product(x) for x in self.positive_roots()])
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 875)
from sage.rings.integer import Integer
7d693534 (Nicolas M. Thiery 2012-03-19 21:38:26 +0100 876)
return Integer(n/d)
}}}
But in any case, someone should check!
--
Ticket URL: <http://trac.sagemath.org/ticket/18453#comment:19>
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