Crystal structure of level zero extremal weight modules

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Abstract

We consider the crystal structure of the level zero extremal weight modules V(λ) using the crystal base of the quantum affine algebra constructed in Duke Math. J. 99 (1999), 455-487. This approach yields an explicit form for extremal weight vectors in the U- part of each connected component of the crystal, which are given as Schur functions in the imaginary root vectors. We show the map Φλ, induces a correspondence between the global crystal base of V(λ) and elements sc0(z-1)G(b), b ∈ B0(Uq[z±1i,k]u′).

Original languageEnglish
Pages (from-to)221-229
Number of pages9
JournalLetters in Mathematical Physics
Volume61
Issue number3
DOIs
StatePublished - Sep 2002

Keywords

  • Crystal base
  • Quantum affine algebra

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