Higher Level Affine Crystals and Young Walls
by Kang, Seok-Jin; Lee, Hyeonmi
Using combinatorics of Young walls, we give a new realization of arbitrary level irreducible highest weight crystals $\mathcal{B}(\lambda)$ for quantum affine algebras of type $A_{\,n}^{(1)}$, $B_n^{(1)}$, $C_n^{(1)}$, $A_{\,2n-1}^{(2)}$, $A_{\,2n}^{(2)}$, and $D_{n+1}^{(2)}$. 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.
DOI: 10.1007/s10468-006-9013-6
Online Date: 7/25/2006
Print publication date: 12/1/2006
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