Higher level affine crystals and Young walls

Details Higher level affine crystals and Young walls Higher level affine crystals and Young walls

2003-10-28

arxiv.org/abs/math/0310430v2

Mathematics

Quantum Algebra

Scientific paper

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 constructions of crystal graphs.

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