Affine crystals of type $D_n^{(1)}$ and Young walls
Abstract
Description
We give a new realization of arbitrary level perfect crystals and arbitrary level irreducible highest weight crystals of type $D_n^{(1)}$, in the language of Young walls. The notions of splitting of blocks and slices play crucial roles in the construction of crystals. The perfect crystals are realized as the set of equivalence classes of slices. And the irreducible highest weight crystals are realized as the affine crystals consisting of reduced proper Young walls which, in turn, are concatenations of slices.