Adjoint crystals and Young walls for

We develop the combinatorics of Young walls associated with higher level adjoint crystals for the quantum affine algebra U q ( s l 2 ̂ ) . The irreducible highest weight crystal B ( λ ) of arbitrary level is realized as the affine crystal consisting of reduced Young walls on λ . We also give a Young wall realization of the crystal B ( ∞ ) for U q − ( s l 2 ̂ ) .