Crystal bases of the Fock space representations and string functions

Let be the quantum affine algebra of type An(1), A2n−1(2), A2n(2), Bn(1), Dn(1), and Dn+1(2), and let be the Fock space representation for a level 1 dominant integral weight Λ. Using the crystal basis of and its characterization in terms of abacus, we construct an explicit bijection between the set of weight vectors in (m 0) for a maximal weight λ and the set of certain ordered sequences of partitions. As a corollary, we obtain the string function of the basic representation V(Λ).