Quiver varieties and path realizations arising from adjoint crystals of type A(1) n

Seok Jin Kang, Euiyong Park

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Let B(Λ0) be the level 1 highest weight crystal of the quantum affine algebra Uq(A(1) n). We construct an explicit crystal isomorphism between the geometric realization B(Λ0) of B(Λ0) via quiver varieties and the path realization Pad(Λ0) of B(Λ0) arising from the adjoint crystal Bad.

Original languageEnglish
Pages (from-to)5341-5366
Number of pages26
JournalTransactions of the American Mathematical Society
Issue number10
StatePublished - Oct 2011


  • Adjoint crystal
  • Crystal graph
  • Kac-moody algebra
  • Path realization
  • Quiver variety

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