Quiver varieties and adjoint crystals of level ℓ for type An(1)

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Let B(Λ) be a level ℓ highest weight crystal of the quantum affine algebra Uq(An(1)). We construct an explicit crystal isomorphism between the geometric realization B(Λ) of the crystal B(Λ) using quiver varieties and the path realization Pad(Λ) arising from the adjoint crystal Bad,ℓ of level ℓ.

Original languageEnglish
Pages (from-to)4513-4539
Number of pages27
JournalCommunications in Algebra
Issue number12
StatePublished - 2012


  • Adjoint crystals
  • Crystal graphs
  • Quiver varieties

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