On the Connection between Young Walls and Littelmann Paths

In the article [7], we developed the combinatorics of Young walls associated with higher level adjoint crystals for the quantum affine algebra Uq(ŝl2). The irreducible highest weight crystal B(λ) of arbitrary level is realized as the affine crystal consisting of reduced Young walls on λ. Littelmann [20] gave a concrete path model with which Joseph and Kashiwara proved that there exists an isomorphism between the crystal graph and the Littelmann paths graph. In this article, using the Young wall constructed in [7] we try to give in combinatorial way the bijective correspondence between the the affine crystal consisting of reduced Young walls on Λ0 and the Littelmann Path model.