#3663: add support for affine crystals
---------------------------+------------------------------------------------
Reporter: mhansen | Owner: aschilling
Type: enhancement | Status: new
Priority: major | Milestone: sage-combinat
Component: combinatorics | Keywords: affine crystals
Reviewer: Dan Bump | Author: Anne Schilling, Brant Jones
Merged: |
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Description changed by aschilling:
Old description:
> Implementation of affine crystals from classical crystals:
> - input is a classical crystal
> - an affine crystal can be constructed by providing the methods e0 and f0
>
> Implementation of affine crystals from classical crystal and promotion:
> - input is a classical crystal and a promotion operators which
> corresponds
> to a Dynkin diagram automorphism
> - the methods e0 and f0 are computed using the promotion operator
>
> Implementation of Kirillov Reshetikhin crystals:
>
> - Type A_n^{(1)} KR crystals are implemented.
> - Type D_n^{(1)}, B_n^{(1)}, A_{2n-1}^{(2)} KR crystals are implemented
> using plus-minus diagrams
> to construct the promotion operator which corresponds to interchanging
> nodes 0 and 1
> - Type C_n^{(1)} KR crystals are implemented; the methods e0 and f0 are
> constructed
> using an embedding into the ambient crystal of type A_{2n+1}^{(2)}
> - Type A_{2n}^{(2)}, D_{n+1}^{(2)} KR crystals are implemented; the
> methods e0 and f0 are
> constructed using an embedding into the ambient crystal of type
> C_n^{(1)} via a similarity
> of crystals
>
> Depends on trac ticket #4326 on root systems.
>
> This patch is authored by Brant Jones and Anne Schilling.
New description:
Implementation of affine crystals from classical crystals:
- input is a classical crystal
- an affine crystal can be constructed by providing the methods e0 and f0
Implementation of affine crystals from classical crystal and promotion:
- input is a classical crystal and a promotion operators which corresponds
to a Dynkin diagram automorphism
- the methods e0 and f0 are computed using the promotion operator
Implementation of Kirillov Reshetikhin crystals:
- Type A_n^{(1)} KR crystals are implemented.
- Type D_n^{(1)}, B_n^{(1)}, A_{2n-1}^{(2)} KR crystals are implemented
using plus-minus diagrams
to construct the promotion operator which corresponds to interchanging
nodes 0 and 1
- Type C_n^{(1)} KR crystals are implemented; the methods e0 and f0 are
constructed
using an embedding into the ambient crystal of type A_{2n+1}^{(2)}
- Type A_{2n}^{(2)}, D_{n+1}^{(2)} KR crystals are implemented; the
methods e0 and f0 are
constructed using an embedding into the ambient crystal of type
C_n^{(1)} via a similarity
of crystals
Some documentation links improvements.
Depends on trac ticket #4326 on root systems.
This patch is authored by Brant Jones and Anne Schilling.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3663#comment:7>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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