#18453: Infinite affine crystals should use extended weight lattice
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Reporter: bump | Owner:
Type: defect | Status: closed
Priority: major | Milestone: sage-6.8
Component: combinatorics | Resolution: fixed
Keywords: crystals, days65 | Merged in:
Authors: Ben Salisbury, Anne | Reviewers: Dan Bump
Schilling, Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
ee398efc22755947ea98f0a8250333d21352f2db |
Dependencies: |
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Changes (by nthiery):
* commit: ee398efc22755947ea98f0a8250333d21352f2db =>
Comment:
Replying to [comment:19 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)
> }}}
This got me curious about my memory failing. Digging back in history ended
up in a mercurial patch from early 2008 from which one can't extract the
author. As far as I remember, I refactored this code at different
occasions (in the above to move it from
weight_lattice_realization to weight_lattice_realizations when
creating the categories), but the original code was by Dan in the
`WeylDim` function. Anyway just ranting this has no relevance.
--
Ticket URL: <http://trac.sagemath.org/ticket/18453#comment:61>
Sage <http://www.sagemath.org>
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