Nakajima monomials, Young walls and Kashiwara embedding for

In this paper, we realize the crystal basis B(λ) of the irreducible highest weight module V(λ) of level 1 for using Nakajima monomials satisfying some conditions. Also, from this monomial realization, we obtain the image of Kashiwara embedding , where ι is some infinite sequence from the index set of simple roots. Finally, we give a -crystal isomorphism between Young wall realization and monomial realization, and so we can understand the image of Kashiwara embedding using the combinatorics of Young walls.