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hal-00682738, version 1

Rank 2 affine MV polytopes

Pierre Baumann 1, Thomas Dunlap 2, Joel Kamnitzer 3, Peter Tingley 4

(28/02/2012)

Résumé : We give a realization of the infinity crystal for affine sl(2) using decorated polygons. The construction and proof are combinatorial, making use of Kashiwara and Saito's characterization of the infinity crystal in terms of the * involution. The polygons we use have combinatorial properties suggesting they are the analogues in this case of the Mirkovic-Vilonen polytopes defined by Anderson and the third author in finite type. Using Kashiwara's similarity of crystals we also give MV polytopes for $A_2^{(2)}$, the only other rank two affine Kac-Moody algebra.

  • 1 :  Institut de Recherche Mathématique Avancée (IRMA)
  • CNRS : UMR7501 – Université de Strasbourg
  • 2 :  Einstein Institute of Mathematics
  • The Hebrew University of Jerusalem
  • 3 :  Department of Mathematics - University of Toronto
  • University of Toronto
  • 4 :  Department of Mathematics [MIT]
  • Massachussetts Institute of Technology (MIT)
  • Domaine : Mathématiques/Combinatoire
    Mathématiques/Algèbres quantiques
  • Mots-clés : crystal basis – affine Lie algebra
 
  • hal-00682738, version 1
  • http://hal.archives-ouvertes.fr/hal-00682738
  • oai:hal.archives-ouvertes.fr:hal-00682738
  • Contributeur : Pierre Baumann <>
  • Soumis le : Lundi 26 Mars 2012, 16:07:12
  • Dernière modification le : Lundi 26 Mars 2012, 16:07:12