Young wall model for $A_2^{(2)}$-type adjoint crystals

We construct a Young wall model for higher level $A_2^{(2)}$-type adjoint crystals. The Young walls and reduced Young walls are defined in connection with affin energy function. We prove that the affine crystal consisiting of reduced Young walls provides a realization of highest weight crystals $B(\lambda )$ and $B(\mathrm{\infty })$.