Adjoint crystals and Young walls for Uq(sl2̂)

We develop the combinatorics of Young walls associated with higher level adjoint crystals for the quantum affine algebra Uq(sl2̂). The irreducible highest weight crystal B(λ)B(λ) of arbitrary level is realized as the affine crystal consisting of reduced Young walls on λλ. We also give a Young wall realization of the crystal B(∞)B(∞) for Uq−(sl2̂).