Crystal structure of level zero extremal weight modules

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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
Issue number3
StatePublished - Sep 2002


  • Crystal base
  • Quantum affine algebra


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