#19139: Implement categories for KR crystals
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.9
Component: combinatorics | Keywords: crystals, KR
Merged in: | Authors: Travis Scrimshaw
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The aim of this ticket is to implement a category for KR crystals and
their tensor products. We do so by implementing a category for (abstract)
U,,q,,'(''g'')-crystals, which I have called
`AffineDerivedSubaglebraCrystals`. Tthere will be a regular affine derived
subalgebra crystals subcategory, and from that, the subcategories with be
KR crystals and their tensor products (which do not have a subcategory
relationship).
This allows for a uniform interface for all KR crystals, allowing us to
define things like `energy_function` for only tensor products of KR
crystals where we don't have to check types. This also makes the default
weight lattice for general crystals of affine type be the extended affine
weight lattice, but anything in the affine derived subalgebra category
will use the non-extended weight lattice. As a consequence, it removes
duplication of trivial `weight_lattice_realization` methods. This category
also allows a better interface which to draw 0-arrows in reverse for
digraphs.
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Ticket URL: <http://trac.sagemath.org/ticket/19139>
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