#8154: Enhancement for crystals
------------------------------+---------------------------------------------
Reporter: aschilling | Owner: sage-combinat
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-4.3.3
Component: combinatorics | Keywords: combinatorics, crystals, KR
crystals
Author: Anne Schilling | Upstream: N/A
Reviewer: Daniel Bump | Merged:
Work_issues: |
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Changes (by bump):
* status: needs_review => positive_review
* milestone: => sage-4.3.3
Comment:
The patch (which goes on top of #7978) applies cleanly to Sage 4.3.2. It
passes sage -testall.
I also tested various things to my satisfaction.
The Demazure operators can be described at two different levels: either as
difference
operators on the weight space or (following Littelmann) as operators on
the crystal.
Here they are implemented as operators on the crystal. They seem to work
correctly.
Later it might be useful to implement them independently in
sage.combinat.root_systems.weyl_characters in the WeightRing.
The direct sums of crystals are implemented.This is essentially just the
disjoint
union. One point is that if two component crystals are equal, a "keepkey"
can be
used to paint them different colors. Then the disjoint union produces a
multiset.
This scheme is inherited from the parent class DisjointUnionEnumeratedSets
where
it is noted that it is subject to future change. I suppose this could be
improved
but that changes must first come in
sage.sets.disjoint_union_enumerated_set.py.
The framework for general highest weight crystals is important. Currently
one can
produce all finite highest weight crystals for types A,B,C,D and G2, but
one must know how to do it.
For types A and C, the CrystalOfTableaux is sufficient but for types B and
D one has half integral
weights and crystals with half-integral highest weight must be created by
tensoring a spin crystal
with a CrystalOfTableaux. The framework in highest_weight.py is a step
towards making this easier.
It should not be hard to implement this for the finite classical Cartan
types.
Various other enhancements and fixes.
I tested the patch to my satisfaction and recommend merging it.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8154#comment:7>
Sage <http://www.sagemath.org>
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