#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, days65 | Merged in:
Authors: Ben Salisbury, | Reviewers:
Anne Schilling, Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 3b3c0b2d15289a8c4a5c5c25ad2984114a856916
public/crystal/18453 | Stopgaps:
Dependencies: |
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Changes (by bsalisbury1):
* cc: ptingley (added)
* keywords: crystals => crystals, days65
Comment:
It seems the original error in the monomial crystals code is due to an
error in the literature about how the weight function is defined for
monomial crystals. I've checked
- Kang, Kim, and Shin, ''Modified Nakajima monomials and the crystal
B(infinity),'' J. Alg. 308 (2007), 524-535.
- Kashiwara, ''Realizations of crystals,'' Contemporary Math. 325 (2003),
133-139.
- Kim and Shin, ''Nakajima monomials, Young walls, and the Kashiwara
embedding,'' J. Alg. 330 (2011), 234-250.
- Kim, ''Monomial realization of crystal graphs for Uq(An1),'' Math. Ann.
332 (2005), 17-35.
- ...
In none of these references is there a way to get `delta` to appear as a
weight. Perhaps I've missed a reference that does include this
information, but I'm thinking about the problem now and planning to
discuss it with Peter TIngley, so hopefully we will have a resolution
soon.
--
Ticket URL: <http://trac.sagemath.org/ticket/18453#comment:22>
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