Crystal Structure of Level Zero Extremal Weight Modules

We consider the crystal structure of the level zero extremal weight modules V() 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 induces a correspondence between the global crystal base of V() and elements .