Using combinatorics of Young walls, we give a new realization of arbitrary level irreducible highest weight crystals $\mathcal{ B}(\lambda)$ for quantum affine algebras of type $A_n^{ (1)}$, $B_n^{ (1)}$, $C_n^{ (1)}$, $A_{ 2n-1}^{ (2)}$, $A_{ 2n}^{ (2)}$, and $D_{ n+1}^{ (2)}$. The irreducible highest weight crystals are realized as the affine crystals consisting of reduced proper Young walls. The notion of slices and splitting of blocks plays a crucial role in the constructions of crystal graphs.
Categories: math.QA