Modified Nakajima monomials and the crystal B (∞)

Seok Jin Kang, Jeong Ah Kim, Dong Uy Shin

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

In this paper, we give a new realization of the crystal B (∞) using modified Nakajima monomials. For the quantum affine algebras of type An(1), we give an explicit characterization of the monomials in B (∞), and construct a natural crystal isomorphism between monomial realization and path realization. As a corollary, we obtain a new realization of the crystal B (∞) for the quantum classical algebras of type An.

Original languageEnglish
Pages (from-to)524-535
Number of pages12
JournalJournal of Algebra
Volume308
Issue number2
DOIs
StatePublished - 15 Feb 2007

Keywords

  • Crystal bases
  • Modified Nakajima monomials

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