Affine crystals of type $D_n^{(1)}$ and Young walls

Details Affine crystals of type $D_n^{(1)}$ and Young walls Affine crystals of type $D_n^{(1)}$ and Young walls

2004-04-19

arxiv.org/abs/math/0404324v1

Mathematics

Quantum Algebra

Scientific paper

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.

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