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Higher level affine crystals and Young walls

Seok-Jin Kang·Hyeonmi Lee
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Abstract

Using combinatorics of Young walls, we give a new realization of arbitrary level irreducible highest weight crystals $\mathcal{B}(λ)$ 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 constructions of crystal graphs.

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Seok-Jin Kang, Hyeonmi Lee. 2003-12-24. Higher level affine crystals and Young walls. https://arxiv.org/abs/math/0310430

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