#14252: Implementation of quantum LS paths
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Reporter: aschilling | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.9
Component: combinatorics | Resolution:
Keywords: crystals, KR crystals | Work issues:
Report Upstream: N/A | Reviewers: Mark Shimozono
Authors: Anne Schilling | Merged in:
Dependencies: | Stopgaps:
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Comment (by mshimo):
I propose the implementation of the crystal class
CrystalOfProjectedLevelZeroLSPaths
that takes as input an affine Cartan type and an element of its
finite weight space.
The result should be paths in the finite weight space,
together with a function that can recover the head and tail energy.
These crystals should know that they are finite as well.
KirillovReshetikhinCrystalFromLSPaths can be an instance of it.
One could doctest CrystalOfProjectedLevelZeroLSPaths
by isomorphism with tensor products of its single-column versions.
Another interesting function would be to write the Naito-Sagaki lift from
KirillovReshetikhinCrystalFromLSPaths
to the level zero LS paths living in the level zero affine weight lattice
(with the null root). Perhaps that is the way the energy function should
be
implemented.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14252#comment:4>
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