Zigzag strip bundles and highest weight crystals

Jeong Ah Kim, Dong Uy Shin

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Zigzag strip bundles are new combinatorial models realizing the crystals B( ∞) for the quantum affine algebras Uq(g), where g=Bn(1),Dn(1),Dn+1(2),Cn(1),A2n-1(2),A2n(2). In this paper, we give new realizations of the crystal bases B(λ) for the irreducible highest weight modules V(λ) over quantum affine algebras Uq(g) using zigzag strip bundles. Further, we discuss the connection between zigzag strip bundle realization, Nakajima monomial realization, and polyhedral realization of the crystals B(λ).

Original languageEnglish
Pages (from-to)15-50
Number of pages36
JournalJournal of Algebra
Volume412
DOIs
StatePublished - 2014 Aug 15

Fingerprint

Zigzag
Strip
Quantum Affine Algebra
Bundle
Crystal
Crystal Bases
Monomial
Module
Model

Keywords

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

Cite this

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Zigzag strip bundles and highest weight crystals. / Kim, Jeong Ah; Shin, Dong Uy.

In: Journal of Algebra, Vol. 412, 15.08.2014, p. 15-50.

Research output: Contribution to journalArticle

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AU - Shin, Dong Uy

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