#3663: add support for affine crystals [with patch, positive review]
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Reporter: mhansen | Owner: aschilling
Type: enhancement | Status: new
Priority: major | Milestone: sage-combinat
Component: combinatorics | Keywords: affine crystals
Work_issues: | Author: Anne Schilling, Brant Jones
Reviewer: Dan Bump | Merged:
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Comment(by bump):
I am reviewing the version of the patch that is in the combinat queue,
running under sage 4.1.1.
I ran {{{sage -testall}}}.
The patch introduces no new failures. (Where it appears in the queue there
are some failures, but the same failures still occur if you qpop the
patch, rebuild and run testall again, so they are not caused by this
patch.)
All new methods have docstrings and tests.
Kirillov-Reshetikhin crystals for are crystal bases on modules of
quantized enveloping algebras of affine Kac-Moody Lie algebras. They had
their origin in the observation that it was sometimes possible to define
crystal bases on the data parametrizing the eigenstates in the Bethe
Ansatz. Beyond that, they tend to be perfect crystals, from which all
integrable modules of the quantum group can be constructed. There is one
Kirillov-Reshetikhin crystal {{{B(r,s)}}} based on tableaux of rectangular
shape {{{s^r}}} for every positive integer s and index r of the underlying
classical crystal.
Constructions of all for the classical untwisted and untwisted types are
summarized in Fourier, Schilling and Okado
http://front.math.ucdavis.edu/0811.1604. Most but all of these are
implemented in sage by this patch.
The unimplemented crystals are listed here: http://groups.google.com/group
/sage-combinat-devel/msg/9571cf3991bca4db?hl=en
I generated quite a few of these and ran {{{C.check()}}} on them. I looked
at a few of them more closely. I am confident that the patch is correct.
It is also an important advance to have these affine crystals in sage.
Some useful functionality is also added in {{{crystals.py}}}. Namely,
morphisms of crystals and some root string operations.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3663#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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