Adjoint crystals and Young walls for \(U_q(\widehat{sl}_2)\) (Q966130)

The authors develop the combinatorics of Young walls associated with higher level adjoint crystals for the quantum affine algebra \(U_q(\widehat{sl}_2)\). The irreducible highest weight crystal \(B(\lambda )\) of arbitrary level is realized as the affine crystal consisting of reduced Young walls on \(\lambda \). A Young wall realization of the crystal \(B(\infty )\) for \(U_q^-(\widehat{sl}_2)\) is also given.