#17055: Implement bijection between RC and MLT for B infinity
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: combinatorics | Resolution:
Keywords: crystals, rigged | Merged in:
configurations, B infinity | Reviewers: Ben Salisbury
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 181fbabd2ea8f6d11226d0c3bab21c7a67db440a
public/crystals/b_infinity_bijection-17055| Stopgaps:
Dependencies: #17054 |
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Changes (by tscrim):
* status: needs_work => needs_review
Comment:
Okay, it all works now.
There seems to be something subtle going on with using the type C
virtualization for the crystal operators and making us use the type
C^(1)^,,n,, bijection (as opposed to the A^(2)^,,2n-1,, bijection). This
seems to be related to the different scaling factors giving rise to
different representations of the crystal. I always had thought this was a
possibility, but it's good to have a confirmed example:
{{{
sage: RCP = RiggedConfigurations(['A',7,2], [[3,1]])
sage: ascii_art(RCP.module_generators[0].f_string([3,4]))
(/) (/) 1[ ]1 -1[ ]-1
sage: RCP = RiggedConfigurations(['C',4,1], [[3,1]])
sage: ascii_art(RCP.module_generators[0].f_string([3,4]))
(/) (/) 0[ ]0 -1[ ]-1
}}}
(but there is still an isomorphism of [classical] crystals on the largest
component).
--
Ticket URL: <http://trac.sagemath.org/ticket/17055#comment:11>
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