Higher level affine crystals and Young walls

Abstract

Using combinatorics of Young walls, we give a new realization of arbitrary level irreducible highest weight crystals B(\lambda) for quantum affine algebras of type A^(1)_n, B^(1)_n, C^(1)_n , A^(2)_2n−1, A^(2)_2n, and D^(2)_n+1. 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 construction of crystals.