Crystal bases of the Fock space representations and string functions

Seok-Jin Kang, Jae-Hoon Kwon

Let $U_q(\mathfrak{g})$ a the quantum affine algebra of type $A_n^{(1)}$, $A_{2n-1}^{(2)}$, $A_{2n}^{(2)}$, $B_n^{(1)}$, $D_n^{(1)}$ and $D_{n+1}^{(2)}$, and let $\mathcal{F}(\Lambda )$ be th…