TY - JOUR
T1 - Crystal structure of level zero extremal weight modules
AU - Beck, Jonathan
PY - 2002/9
Y1 - 2002/9
N2 - 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′).
AB - 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′).
KW - Crystal base
KW - Quantum affine algebra
UR - http://www.scopus.com/inward/record.url?scp=0039484745&partnerID=8YFLogxK
U2 - 10.1023/A:1021212622438
DO - 10.1023/A:1021212622438
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AN - SCOPUS:0039484745
SN - 0377-9017
VL - 61
SP - 221
EP - 229
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 3
ER -