Zigzag strip bundles and crystals

Jeong Ah Kim, Dong Uy Shin

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We introduce new combinatorial models, called zigzag strip bundles, over quantum affine algebras Uq(Bn(1)), Uq(Dn(1)) and Uq(Dn+1(2)), and show that the sets of all zigzag strip bundles for Uq(Bn(1)), Uq(Dn(1)) and Uq(Dn+1(2)) realize the crystal bases B( ∞ ) of Uq-(Bn(1)), Uq-(Dn(1)) and Uq-(Dn+1(2)), respectively. Further, we discuss the connection between zigzag strip bundle realization, Nakajima monomial realization, and polyhedral realization of the crystal B( ∞ ).

Original languageEnglish
Pages (from-to)1087-1115
Number of pages29
JournalJournal of Combinatorial Theory. Series A
Issue number5
StatePublished - Jul 2013


  • Crystals
  • Kashiwara embeddings
  • Nakajima monomials
  • Zigzag strip bundles


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