Opened 11 years ago

Last modified 10 years ago

#3663 closed enhancement

add support for affine crystals — at Version 5

Reported by: mhansen Owned by: aschilling
Priority: major Milestone: sage-4.3
Component: combinatorics Keywords: affine crystals
Cc: sage-combinat, bump@… Merged in:
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Report Upstream: N/A Work issues:
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Description (last modified by aschilling)

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.

Change History (8)

comment:1 Changed 10 years ago by nthiery

  • Cc sage-combinat added

Changed 10 years ago by aschilling

comment:2 Changed 10 years ago by aschilling

  • Description modified (diff)
  • Keywords affine crystals added
  • Owner changed from mhansen to aschilling

comment:3 Changed 10 years ago by aschilling

  • Description modified (diff)

Changed 10 years ago by aschilling

comment:4 Changed 10 years ago by aschilling

  • Description modified (diff)

comment:5 Changed 10 years ago by aschilling

  • Description modified (diff)

Changed 10 years ago by aschilling

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